#! /usr/bin/env python # def laguerre_set ( n ): #*****************************************************************************80 # ## LAGUERRE_SET sets abscissas and weights for Laguerre quadrature. # # Discussion: # # The abscissas are the zeroes of the Laguerre polynomial L(N)(X). # # The integral: # # Integral ( 0 <= X < +oo ) exp ( -X ) * F(X) dX # # The quadrature rule: # # Sum ( 1 <= I <= N ) W(I) * f ( X(I) ) # # The integral: # # Integral ( 0 <= X < +oo ) F(X) dX # # The quadrature rule: # # Sum ( 1 <= I <= N ) W(I) * exp ( X(I) ) * f ( X(I) ) # # Mathematica can numerically estimate the abscissas for the # n-th order polynomial to p digits of precision by the command: # # NSolve [ LaguerreL[n,x] == 0, x, p ] # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 15 June 2015 # # Author: # # John Burkardt # # Reference: # # Milton Abramowitz, Irene Stegun, # Handbook of Mathematical Functions, # National Bureau of Standards, 1964, # ISBN: 0-486-61272-4, # LC: QA47.A34. # # Vladimir Krylov, # Approximate Calculation of Integrals, # Dover, 2006, # ISBN: 0486445798, # LC: QA311.K713. # # Arthur Stroud, Don Secrest, # Gaussian Quadrature Formulas, # Prentice Hall, 1966, # LC: QA299.4G3S7. # # Stephen Wolfram, # The Mathematica Book, # Fourth Edition, # Cambridge University Press, 1999, # ISBN: 0-521-64314-7, # LC: QA76.95.W65. # # Daniel Zwillinger, editor, # CRC Standard Mathematical Tables and Formulae, # 30th Edition, # CRC Press, 1996, # ISBN: 0-8493-2479-3, # LC: QA47.M315. # # Parameters: # # Input, integer N, the order. # N must be between 1 and 20, 31/32/33, 63/64/65, 127/128/129. # # Output, real X(N), the abscissas. # # Output, real W(N), the weights. # import numpy as np from sys import exit if ( n == 1 ): x = np.array ( [ \ 1.00000000000000000000000000000E+00 ] ) w = np.array ( [ \ 1.00000000000000000000000000000E+00 ] ) elif ( n == 2 ): x = np.array ( [ \ 0.585786437626904951198311275790E+00, \ 3.41421356237309504880168872421E+00 ] ) w = np.array ( [ \ 0.85355339059327376220042218105E+00, \ 0.146446609406726237799577818948E+00 ] ) elif ( n == 3 ): x = np.array ( [ \ 0.415774556783479083311533873128E+00, \ 2.29428036027904171982205036136E+00, \ 6.28994508293747919686641576551E+00 ] ) w = np.array ( [ \ 0.71109300992917301544959019114E+00, \ 0.27851773356924084880144488846E+00, \ 0.010389256501586135748964920401E+00 ] ) elif ( n == 4 ): x = np.array ( [ \ 0.322547689619392311800361459104E+00, \ 1.74576110115834657568681671252E+00, \ 4.53662029692112798327928538496E+00, \ 9.39507091230113312923353644342E+00 ] ) w = np.array ( [ \ 0.60315410434163360163596602382E+00, \ 0.35741869243779968664149201746E+00, \ 0.03888790851500538427243816816E+00, \ 0.0005392947055613274501037905676E+00 ] ) elif ( n == 5 ): x = np.array ( [ \ 0.263560319718140910203061943361E+00, \ 1.41340305910651679221840798019E+00, \ 3.59642577104072208122318658878E+00, \ 7.08581000585883755692212418111E+00, \ 12.6408008442757826594332193066E+00 ] ) w = np.array ( [ \ 0.52175561058280865247586092879E+00, \ 0.3986668110831759274541333481E+00, \ 0.0759424496817075953876533114E+00, \ 0.00361175867992204845446126257E+00, \ 0.00002336997238577622789114908455E+00 ] ) elif ( n == 6 ): x = np.array ( [ \ 0.222846604179260689464354826787E+00, \ 1.18893210167262303074315092194E+00, \ 2.99273632605931407769132528451E+00, \ 5.77514356910451050183983036943E+00, \ 9.83746741838258991771554702994E+00, \ 15.9828739806017017825457915674E+00 ] ) w = np.array ( [ \ 0.45896467394996359356828487771E+00, \ 0.4170008307721209941133775662E+00, \ 0.1133733820740449757387061851E+00, \ 0.01039919745314907489891330285E+00, \ 0.000261017202814932059479242860E+00, \ 8.98547906429621238825292053E-07 ] ) elif ( n == 7 ): x = np.array ( [ \ 0.193043676560362413838247885004E+00, \ 1.02666489533919195034519944317E+00, \ 2.56787674495074620690778622666E+00, \ 4.90035308452648456810171437810E+00, \ 8.18215344456286079108182755123E+00, \ 12.7341802917978137580126424582E+00, \ 19.3957278622625403117125820576E+00 ] ) w = np.array ( [ \ 0.40931895170127390213043288002E+00, \ 0.4218312778617197799292810054E+00, \ 0.1471263486575052783953741846E+00, \ 0.0206335144687169398657056150E+00, \ 0.00107401014328074552213195963E+00, \ 0.0000158654643485642012687326223E+00, \ 3.17031547899558056227132215E-08 ] ) elif ( n == 8 ): x = np.array ( [ \ 0.170279632305100999788861856608E+00, \ 0.903701776799379912186020223555E+00, \ 2.25108662986613068930711836697E+00, \ 4.26670017028765879364942182690E+00, \ 7.04590540239346569727932548212E+00, \ 10.7585160101809952240599567880E+00, \ 15.7406786412780045780287611584E+00, \ 22.8631317368892641057005342974E+00 ] ) w = np.array ( [ \ 0.36918858934163752992058283938E+00, \ 0.4187867808143429560769785813E+00, \ 0.175794986637171805699659867E+00, \ 0.033343492261215651522132535E+00, \ 0.0027945362352256725249389241E+00, \ 0.00009076508773358213104238501E+00, \ 8.4857467162725315448680183E-07, \ 1.04800117487151038161508854E-09 ] ) elif ( n == 9 ): x = np.array ( [ \ 0.152322227731808247428107073127E+00, \ 0.807220022742255847741419210952E+00, \ 2.00513515561934712298303324701E+00, \ 3.78347397333123299167540609364E+00, \ 6.20495677787661260697353521006E+00, \ 9.37298525168757620180971073215E+00, \ 13.4662369110920935710978818397E+00, \ 18.8335977889916966141498992996E+00, \ 26.3740718909273767961410072937E+00 ] ) w = np.array ( [ \ 0.336126421797962519673467717606E+00, \ 0.411213980423984387309146942793E+00, \ 0.199287525370885580860575607212E+00, \ 0.0474605627656515992621163600479E+00, \ 0.00559962661079458317700419900556E+00, \ 0.000305249767093210566305412824291E+00, \ 6.59212302607535239225572284875E-06, \ 4.1107693303495484429024104033E-08, \ 3.29087403035070757646681380323E-11 ] ) elif ( n == 10 ): x = np.array ( [ \ 0.137793470540492430830772505653E+00, \ 0.729454549503170498160373121676E+00, \ 1.80834290174031604823292007575E+00, \ 3.40143369785489951448253222141E+00, \ 5.55249614006380363241755848687E+00, \ 8.33015274676449670023876719727E+00, \ 11.8437858379000655649185389191E+00, \ 16.2792578313781020995326539358E+00, \ 21.9965858119807619512770901956E+00, \ 29.9206970122738915599087933408E+00 ] ) w = np.array ( [ \ 0.30844111576502014154747083468E+00, \ 0.4011199291552735515157803099E+00, \ 0.218068287611809421588648523E+00, \ 0.062087456098677747392902129E+00, \ 0.009501516975181100553839072E+00, \ 0.0007530083885875387754559644E+00, \ 0.00002825923349599565567422564E+00, \ 4.249313984962686372586577E-07, \ 1.839564823979630780921535E-09, \ 9.911827219609008558377547E-13 ] ) elif ( n == 11 ): x = np.array ( [ \ 0.125796442187967522675794577516E+00, \ 0.665418255839227841678127839420E+00, \ 1.64715054587216930958700321365E+00, \ 3.09113814303525495330195934259E+00, \ 5.02928440157983321236999508366E+00, \ 7.50988786380661681941099714450E+00, \ 10.6059509995469677805559216457E+00, \ 14.4316137580641855353200450349E+00, \ 19.1788574032146786478174853989E+00, \ 25.2177093396775611040909447797E+00, \ 33.4971928471755372731917259395E+00 ] ) w = np.array ( [ \ 0.28493321289420060505605102472E+00, \ 0.3897208895278493779375535080E+00, \ 0.232781831848991333940223796E+00, \ 0.076564453546196686400854179E+00, \ 0.014393282767350695091863919E+00, \ 0.001518880846484873069847776E+00, \ 0.0000851312243547192259720424E+00, \ 2.29240387957450407857683E-06, \ 2.48635370276779587373391E-08, \ 7.71262693369132047028153E-11, \ 2.883775868323623861597778E-14 ] ) elif ( n == 12 ): x = np.array ( [ \ 0.115722117358020675267196428240E+00, \ 0.611757484515130665391630053042E+00, \ 1.51261026977641878678173792687E+00, \ 2.83375133774350722862747177657E+00, \ 4.59922763941834848460572922485E+00, \ 6.84452545311517734775433041849E+00, \ 9.62131684245686704391238234923E+00, \ 13.0060549933063477203460524294E+00, \ 17.1168551874622557281840528008E+00, \ 22.1510903793970056699218950837E+00, \ 28.4879672509840003125686072325E+00, \ 37.0991210444669203366389142764E+00 ] ) w = np.array ( [ \ 0.26473137105544319034973889206E+00, \ 0.3777592758731379820244905567E+00, \ 0.244082011319877564254870818E+00, \ 0.09044922221168093072750549E+00, \ 0.02010238115463409652266129E+00, \ 0.002663973541865315881054158E+00, \ 0.000203231592662999392121433E+00, \ 8.3650558568197987453363E-06, \ 1.66849387654091026116990E-07, \ 1.34239103051500414552392E-09, \ 3.06160163503502078142408E-12, \ 8.148077467426241682473119E-16 ] ) elif ( n == 13 ): x = np.array ( [ \ 0.107142388472252310648493376977E+00, \ 0.566131899040401853406036347177E+00, \ 1.39856433645101971792750259921E+00, \ 2.61659710840641129808364008472E+00, \ 4.23884592901703327937303389926E+00, \ 6.29225627114007378039376523025E+00, \ 8.81500194118697804733348868036E+00, \ 11.8614035888112425762212021880E+00, \ 15.5107620377037527818478532958E+00, \ 19.8846356638802283332036594634E+00, \ 25.1852638646777580842970297823E+00, \ 31.8003863019472683713663283526E+00, \ 40.7230086692655795658979667001E+00 ] ) w = np.array ( [ \ 0.24718870842996262134624918596E+00, \ 0.3656888229005219453067175309E+00, \ 0.252562420057658502356824289E+00, \ 0.10347075802418370511421863E+00, \ 0.02643275441556161577815877E+00, \ 0.00422039604025475276555209E+00, \ 0.000411881770472734774892473E+00, \ 0.0000235154739815532386882897E+00, \ 7.3173116202490991040105E-07, \ 1.10884162570398067979151E-08, \ 6.7708266922058988406462E-11, \ 1.15997995990507606094507E-13, \ 2.245093203892758415991872E-17 ] ) elif ( n == 14 ): x = np.array ( [ \ 0.0997475070325975745736829452514E+00, \ 0.526857648851902896404583451502E+00, \ 1.30062912125149648170842022116E+00, \ 2.43080107873084463616999751038E+00, \ 3.93210282229321888213134366778E+00, \ 5.82553621830170841933899983898E+00, \ 8.14024014156514503005978046052E+00, \ 10.9164995073660188408130510904E+00, \ 14.2108050111612886831059780825E+00, \ 18.1048922202180984125546272083E+00, \ 22.7233816282696248232280886985E+00, \ 28.2729817232482056954158923218E+00, \ 35.1494436605924265828643121364E+00, \ 44.3660817111174230416312423666E+00 ] ) w = np.array ( [ \ 0.23181557714486497784077486110E+00, \ 0.3537846915975431518023313013E+00, \ 0.258734610245428085987320561E+00, \ 0.11548289355692321008730499E+00, \ 0.03319209215933736003874996E+00, \ 0.00619286943700661021678786E+00, \ 0.00073989037786738594242589E+00, \ 0.000054907194668416983785733E+00, \ 2.4095857640853774967578E-06, \ 5.801543981676495180886E-08, \ 6.819314692484974119616E-10, \ 3.2212077518948479398089E-12, \ 4.2213524405165873515980E-15, \ 6.05237502228918880839871E-19 ] ) elif ( n == 15 ): x = np.array ( [ \ 0.0933078120172818047629030383672E+00, \ 0.492691740301883908960101791412E+00, \ 1.21559541207094946372992716488E+00, \ 2.26994952620374320247421741375E+00, \ 3.66762272175143727724905959436E+00, \ 5.42533662741355316534358132596E+00, \ 7.56591622661306786049739555812E+00, \ 10.1202285680191127347927394568E+00, \ 13.1302824821757235640991204176E+00, \ 16.6544077083299578225202408430E+00, \ 20.7764788994487667729157175676E+00, \ 25.6238942267287801445868285977E+00, \ 31.4075191697539385152432196202E+00, \ 38.5306833064860094162515167595E+00, \ 48.0260855726857943465734308508E+00 ] ) w = np.array ( [ \ 0.21823488594008688985641323645E+00, \ 0.3422101779228833296389489568E+00, \ 0.263027577941680097414812275E+00, \ 0.12642581810593053584303055E+00, \ 0.04020686492100091484158548E+00, \ 0.00856387780361183836391576E+00, \ 0.00121243614721425207621921E+00, \ 0.00011167439234425194199258E+00, \ 6.459926762022900924653E-06, \ 2.226316907096272630332E-07, \ 4.227430384979365007351E-09, \ 3.921897267041089290385E-11, \ 1.4565152640731264063327E-13, \ 1.4830270511133013354616E-16, \ 1.60059490621113323104998E-20 ] ) elif ( n == 16 ): x = np.array ( [ \ 0.0876494104789278403601980973401E+00, \ 0.462696328915080831880838260664E+00, \ 1.14105777483122685687794501811E+00, \ 2.12928364509838061632615907066E+00, \ 3.43708663389320664523510701675E+00, \ 5.07801861454976791292305830814E+00, \ 7.07033853504823413039598947080E+00, \ 9.43831433639193878394724672911E+00, \ 12.2142233688661587369391246088E+00, \ 15.4415273687816170767647741622E+00, \ 19.1801568567531348546631409497E+00, \ 23.5159056939919085318231872752E+00, \ 28.5787297428821403675206137099E+00, \ 34.5833987022866258145276871778E+00, \ 41.9404526476883326354722330252E+00, \ 51.7011603395433183643426971197E+00 ] ) w = np.array ( [ \ 0.20615171495780099433427363674E+00, \ 0.3310578549508841659929830987E+00, \ 0.265795777644214152599502021E+00, \ 0.13629693429637753997554751E+00, \ 0.0473289286941252189780623E+00, \ 0.0112999000803394532312490E+00, \ 0.0018490709435263108642918E+00, \ 0.00020427191530827846012602E+00, \ 0.00001484458687398129877135E+00, \ 6.828319330871199564396E-07, \ 1.881024841079673213882E-08, \ 2.862350242973881619631E-10, \ 2.127079033224102967390E-12, \ 6.297967002517867787174E-15, \ 5.050473700035512820402E-18, \ 4.1614623703728551904265E-22 ] ) elif ( n == 17 ): x = np.array ( [ \ 0.0826382147089476690543986151980E+00, \ 0.436150323558710436375959029847E+00, \ 1.07517657751142857732980316755E+00, \ 2.00519353164923224070293371933E+00, \ 3.23425612404744376157380120696E+00, \ 4.77351351370019726480932076262E+00, \ 6.63782920536495266541643929703E+00, \ 8.84668551116980005369470571184E+00, \ 11.4255293193733525869726151469E+00, \ 14.4078230374813180021982874959E+00, \ 17.8382847307011409290658752412E+00, \ 21.7782682577222653261749080522E+00, \ 26.3153178112487997766149598369E+00, \ 31.5817716804567331343908517497E+00, \ 37.7960938374771007286092846663E+00, \ 45.3757165339889661829258363215E+00, \ 55.3897517898396106640900199790E+00 ] ) w = np.array ( [ \ 0.19533220525177083214592729770E+00, \ 0.3203753572745402813366256320E+00, \ 0.267329726357171097238809604E+00, \ 0.14512985435875862540742645E+00, \ 0.0544369432453384577793806E+00, \ 0.0143572977660618672917767E+00, \ 0.0026628247355727725684324E+00, \ 0.0003436797271562999206118E+00, \ 0.00003027551783782870109437E+00, \ 1.768515053231676895381E-06, \ 6.57627288681043332199E-08, \ 1.469730932159546790344E-09, \ 1.81691036255544979555E-11, \ 1.095401388928687402976E-13, \ 2.617373882223370421551E-16, \ 1.6729356931461546908502E-19, \ 1.06562631627404278815253E-23 ] ) elif ( n == 18 ): x = np.array ( [ \ 0.0781691666697054712986747615334E+00, \ 0.412490085259129291039101536536E+00, \ 1.01652017962353968919093686187E+00, \ 1.89488850996976091426727831954E+00, \ 3.05435311320265975115241130719E+00, \ 4.50420553888989282633795571455E+00, \ 6.25672507394911145274209116326E+00, \ 8.32782515660563002170470261564E+00, \ 10.7379900477576093352179033397E+00, \ 13.5136562075550898190863812108E+00, \ 16.6893062819301059378183984163E+00, \ 20.3107676262677428561313764553E+00, \ 24.4406813592837027656442257980E+00, \ 29.1682086625796161312980677805E+00, \ 34.6279270656601721454012429438E+00, \ 41.0418167728087581392948614284E+00, \ 48.8339227160865227486586093290E+00, \ 59.0905464359012507037157810181E+00 ] ) w = np.array ( [ \ 0.18558860314691880562333775228E+00, \ 0.3101817663702252936495975957E+00, \ 0.267866567148536354820854395E+00, \ 0.15297974746807490655384308E+00, \ 0.0614349178609616527076780E+00, \ 0.0176872130807729312772600E+00, \ 0.0036601797677599177980266E+00, \ 0.0005406227870077353231284E+00, \ 0.0000561696505121423113818E+00, \ 4.01530788370115755859E-06, \ 1.91466985667567497969E-07, \ 5.8360952686315941292E-09, \ 1.07171126695539012773E-10, \ 1.08909871388883385562E-12, \ 5.38666474837830887608E-15, \ 1.049865978035703408779E-17, \ 5.405398451631053643566E-21, \ 2.6916532692010286270838E-25 ] ) elif ( n == 19 ): x = np.array ( [ \ 0.0741587837572050877131369916024E+00, \ 0.391268613319994607337648350299E+00, \ 0.963957343997958058624878377130E+00, \ 1.79617558206832812557725825252E+00, \ 2.89365138187378399116494713237E+00, \ 4.26421553962776647436040018167E+00, \ 5.91814156164404855815360191408E+00, \ 7.86861891533473373105668358176E+00, \ 10.1324237168152659251627415800E+00, \ 12.7308814638423980045092979656E+00, \ 15.6912783398358885454136069861E+00, \ 19.0489932098235501532136429732E+00, \ 22.8508497608294829323930586693E+00, \ 27.1606693274114488789963947149E+00, \ 32.0691222518622423224362865906E+00, \ 37.7129058012196494770647508283E+00, \ 44.3173627958314961196067736013E+00, \ 52.3129024574043831658644222420E+00, \ 62.8024231535003758413504690673E+00 ] ) w = np.array ( [ \ 0.17676847491591250225103547981E+00, \ 0.3004781436072543794821568077E+00, \ 0.267599547038175030772695441E+00, \ 0.15991337213558021678551215E+00, \ 0.0682493799761491134552355E+00, \ 0.0212393076065443249244062E+00, \ 0.0048416273511483959672501E+00, \ 0.0008049127473813667665946E+00, \ 0.0000965247209315350170843E+00, \ 8.20730525805103054409E-06, \ 4.8305667247307725394E-07, \ 1.90499136112328569994E-08, \ 4.8166846309280615577E-10, \ 7.3482588395511443768E-12, \ 6.2022753875726163989E-14, \ 2.54143084301542272372E-16, \ 4.07886129682571235007E-19, \ 1.707750187593837061004E-22, \ 6.715064649908189959990E-27 ] ) elif ( n == 20 ): x = np.array ( [ \ 0.0705398896919887533666890045842E+00, \ 0.372126818001611443794241388761E+00, \ 0.916582102483273564667716277074E+00, \ 1.70730653102834388068768966741E+00, \ 2.74919925530943212964503046049E+00, \ 4.04892531385088692237495336913E+00, \ 5.61517497086161651410453988565E+00, \ 7.45901745367106330976886021837E+00, \ 9.59439286958109677247367273428E+00, \ 12.0388025469643163096234092989E+00, \ 14.8142934426307399785126797100E+00, \ 17.9488955205193760173657909926E+00, \ 21.4787882402850109757351703696E+00, \ 25.4517027931869055035186774846E+00, \ 29.9325546317006120067136561352E+00, \ 35.0134342404790000062849359067E+00, \ 40.8330570567285710620295677078E+00, \ 47.6199940473465021399416271529E+00, \ 55.8107957500638988907507734445E+00, \ 66.5244165256157538186403187915E+00 ] ) w = np.array ( [ \ 0.168746801851113862149223899689E+00, \ 0.291254362006068281716795323812E+00, \ 0.266686102867001288549520868998E+00, \ 0.166002453269506840031469127816E+00, \ 0.0748260646687923705400624639615E+00, \ 0.0249644173092832210728227383234E+00, \ 0.00620255084457223684744754785395E+00, \ 0.00114496238647690824203955356969E+00, \ 0.000155741773027811974779809513214E+00, \ 0.0000154014408652249156893806714048E+00, \ 1.08648636651798235147970004439E-06, \ 5.33012090955671475092780244305E-08, \ 1.7579811790505820035778763784E-09, \ 3.72550240251232087262924585338E-11, \ 4.76752925157819052449488071613E-13, \ 3.37284424336243841236506064991E-15, \ 1.15501433950039883096396247181E-17, \ 1.53952214058234355346383319667E-20, \ 5.28644272556915782880273587683E-24, \ 1.65645661249902329590781908529E-28 ] ) elif ( n == 31 ): x = np.array ( [ \ 0.0459019476211082907434960802752E+00, \ 0.241980163824772048904089741517E+00, \ 0.595253894222350737073301650054E+00, \ 1.10668949953299871621113087898E+00, \ 1.77759569287477272115937274827E+00, \ 2.60970341525668065038933759253E+00, \ 3.60519680234004426988058175542E+00, \ 4.76674708447176113136291272711E+00, \ 6.09755456718174092699254293285E+00, \ 7.60140094923313742293601069429E+00, \ 9.28271431347088941825366952977E+00, \ 11.1466497556192913589938156296E+00, \ 13.1991895762449985224649250286E+00, \ 15.4472683155493100758093258918E+00, \ 17.8989298266447576467257938178E+00, \ 20.5635263367158221707430489688E+00, \ 23.4519734820118585910502555759E+00, \ 26.5770813521182604599758769865E+00, \ 29.9539908723464455069519178400E+00, \ 33.6007595329022027354103138858E+00, \ 37.5391644073304408828879025580E+00, \ 41.7958308701822199813479458533E+00, \ 46.4038668064111231360292276044E+00, \ 51.4053144767977551618614610884E+00, \ 56.8549928687158436205119220557E+00, \ 62.8268559087863214536775233048E+00, \ 69.4252771910803456233222516564E+00, \ 76.8070477638627328376099722855E+00, \ 85.2303586075456691693870656070E+00, \ 95.1889398915256299813086068540E+00, \ 107.952243827578714750024401177E+00 ] ) w = np.array ( [ \ 0.112527895503725838208477280828E+00, \ 0.21552760818089123795222505285E+00, \ 0.238308251645696547319057880892E+00, \ 0.195388309297902292499153033907E+00, \ 0.126982832893061901436352729046E+00, \ 0.0671861689238993006709294419935E+00, \ 0.029303224993879487404888669312E+00, \ 0.0105975699152957360895293803144E+00, \ 0.0031851272582386980320974842433E+00, \ 0.000795495483079403829220921490125E+00, \ 0.000164800521266366873178629671164E+00, \ 0.000028229237864310816393860971469E+00, \ 3.98029025510085803871161749001E-06, \ 4.59318398418010616737296945103E-07, \ 4.30755451877311009301314574659E-08, \ 3.25512499382715708551757492579E-09, \ 1.96202466754105949962471515931E-10, \ 9.31904990866175871295347164313E-12, \ 3.43775418194116205203125978983E-13, \ 9.67952471304467169974050357762E-15, \ 2.03680661101152473980106242193E-16, \ 3.12126872807135268317653586326E-18, \ 3.37295817041610524533956783083E-20, \ 2.46727963866166960110383632425E-22, \ 1.15822019045256436348345645766E-24, \ 3.2472922591425422434798022809E-27, \ 4.91430173080574327408200762597E-30, \ 3.45000711048083941322231359538E-33, \ 8.76637101171620414729327607329E-37, \ 5.03636439211614904112971723166E-41, \ 1.99099845825314564824395490803E-46 ] ) elif ( n == 32 ): x = np.array ( [ \ 0.0444893658332670184188501945244E+00, \ 0.234526109519618537452909561302E+00, \ 0.576884629301886426491552569378E+00, \ 1.07244875381781763304091397718E+00, \ 1.72240877644464544113093292797E+00, \ 2.52833670642579488112419990556E+00, \ 3.49221327302199448960880339977E+00, \ 4.61645676974976738776205229617E+00, \ 5.90395850417424394656152149158E+00, \ 7.35812673318624111322198973719E+00, \ 8.98294092421259610337824752677E+00, \ 10.7830186325399720675019491381E+00, \ 12.7636979867427251149690330822E+00, \ 14.9311397555225573197969646873E+00, \ 17.2924543367153147892357183836E+00, \ 19.8558609403360547397899445841E+00, \ 22.6308890131967744886757793394E+00, \ 25.6286360224592477674761768768E+00, \ 28.8621018163234747443426407115E+00, \ 32.3466291539647370032321654237E+00, \ 36.1004948057519738040171189479E+00, \ 40.1457197715394415362093439289E+00, \ 44.5092079957549379759066043775E+00, \ 49.2243949873086391767222218066E+00, \ 54.3337213333969073328671815512E+00, \ 59.8925091621340181961304753247E+00, \ 65.9753772879350527965630761193E+00, \ 72.6876280906627086386753490878E+00, \ 80.1874469779135230674916385687E+00, \ 88.7353404178923986893554495243E+00, \ 98.8295428682839725591844784095E+00, \ 111.751398097937695213664716539E+00 ] ) w = np.array ( [ \ 0.109218341952384971136131337943E+00, \ 0.210443107938813232936062071392E+00, \ 0.235213229669848005394941106676E+00, \ 0.195903335972881043413247901182E+00, \ 0.129983786286071760607216822326E+00, \ 0.0705786238657174415601643320433E+00, \ 0.0317609125091750703058255211629E+00, \ 0.0119182148348385570565446505756E+00, \ 0.00373881629461152478966122847796E+00, \ 0.000980803306614955132230630611308E+00, \ 0.000214864918801364188023199483686E+00, \ 0.0000392034196798794720432695682782E+00, \ 5.93454161286863287835582893773E-06, \ 7.4164045786675522190708220213E-07, \ 7.60456787912078148111926545943E-08, \ 6.35060222662580674242777108552E-09, \ 4.28138297104092887881360582098E-10, \ 2.30589949189133607927336809618E-11, \ 9.79937928872709406333455225995E-13, \ 3.23780165772926646231042646142E-14, \ 8.17182344342071943320186059177E-16, \ 1.54213383339382337217855949129E-17, \ 2.11979229016361861204093474373E-19, \ 2.05442967378804542665570987602E-21, \ 1.34698258663739515580519340478E-23, \ 5.66129413039735937112634432382E-26, \ 1.41856054546303690595142933892E-28, \ 1.91337549445422430937127829683E-31, \ 1.19224876009822235654164532831E-34, \ 2.67151121924013698599867893958E-38, \ 1.33861694210625628271905701423E-42, \ 4.51053619389897423222342830132E-48 ] ) elif ( n == 33 ): x = np.array ( [ \ 0.0431611356173268921917334738206E+00, \ 0.227517802803371123850290226913E+00, \ 0.559616655851539887586282303916E+00, \ 1.04026850775100205382209621927E+00, \ 1.67055919607571519092562973257E+00, \ 2.45192079589763054651073898192E+00, \ 3.38615533758800483230187851832E+00, \ 4.47545949839977145702059137905E+00, \ 5.72245472027210352266790817933E+00, \ 7.13022434440010801631414039534E+00, \ 8.70235923062140624893696399459E+00, \ 10.4430136502059824268455293839E+00, \ 12.3569737593502859624441255236E+00, \ 14.4497416815855402377145121178E+00, \ 16.7276392186383223532615229942E+00, \ 19.1979365872124466372283088222E+00, \ 21.8690135249281898713512287043E+00, \ 24.7505629061577956433730931987E+00, \ 27.8538511114133567797747375537E+00, \ 31.1920555455751298677734295989E+00, \ 34.7807091535383377002292521853E+00, \ 38.6382967177740302250360622751E+00, \ 42.7870720782534794879639219927E+00, \ 47.2542066029932658172690829767E+00, \ 52.0734519015142202671640200482E+00, \ 57.2876345410929400754514841078E+00, \ 62.9525659469066302071906336861E+00, \ 69.1435133801098924457366348147E+00, \ 75.9666870142470623437939790250E+00, \ 83.5816372232708807614192336050E+00, \ 92.2511394441351012341481184391E+00, \ 102.477844336823322575825984750E+00, \ 115.554756448995807306876850793E+00 ] ) w = np.array ( [ \ 0.106097745553686759448980241986E+00, \ 0.205582983661932603502389046086E+00, \ 0.232126523496060850848680143719E+00, \ 0.196207372769141916829837191484E+00, \ 0.132744856705171098099698375677E+00, \ 0.0738518038877138714048058524075E+00, \ 0.0342232334108640270351258175641E+00, \ 0.0132939751808086665861981468532E+00, \ 0.00434094309504623645941229723703E+00, \ 0.0011922509906686840510776728263E+00, \ 0.000275158225582396584420253012954E+00, \ 0.0000532433409922782412444424323192E+00, \ 8.60957132646331618369236329569E-06, \ 1.15837796102469195604266695945E-06, \ 1.28985114856525884538052927779E-07, \ 1.18096786980325241031580363325E-08, \ 8.82276640967020246770192412272E-10, \ 5.32961213410302701363055555216E-11, \ 2.57550403748317439431393144398E-12, \ 9.8314133225207825980561863437E-14, \ 2.92041495556546845392792035892E-15, \ 6.63077156752381637730149511056E-17, \ 1.12609863704995018019882580368E-18, \ 1.39311657122392009414616980902E-20, \ 1.21481009891544297673141523063E-22, \ 7.16158181142099840535743381278E-25, \ 2.70320712488116872172720734689E-27, \ 6.07192361286922243586897316027E-30, \ 7.32134211132579407517616095945E-33, \ 4.06131706145569795511645700604E-36, \ 8.04952284545203726871355981553E-40, \ 3.52902990360469937522008596417E-44, \ 1.01716656299412569799194166119E-49 ] ) elif ( n == 63 ): x = np.array ( [ \ 0.0227688937325761537859943302486E+00, \ 0.119983252427278247157714164264E+00, \ 0.294941854447701495774277385174E+00, \ 0.547790878962377253638650737759E+00, \ 0.878690611799319016738955670523E+00, \ 1.28784643359197063023092077886E+00, \ 1.77551238153885537639794632687E+00, \ 2.34199255670859892560556283377E+00, \ 2.98764232232464739399767310536E+00, \ 3.71286959920180003462996374134E+00, \ 4.51813633495035843911055685616E+00, \ 5.40396017818259462869025997827E+00, \ 6.37091637878653302203922508918E+00, \ 7.41963993393117111548884931990E+00, \ 8.55082800084033283125890487222E+00, \ 9.76524259992453668070045929780E+00, \ 11.0637136351406617362205504106E+00, \ 12.4471422623564927497986875693E+00, \ 13.9165046410578185629129670082E+00, \ 15.4728561100362964247771436078E+00, \ 17.1173358338635887531169003039E+00, \ 18.8511719741548568508734837875E+00, \ 20.6756874480565156603772656674E+00, \ 22.5923063463115283812922777600E+00, \ 24.6025610949726388837006427600E+00, \ 26.7081004587373439697790879988E+00, \ 28.9106985004513826401777181032E+00, \ 31.2122646311759128854777738208E+00, \ 33.6148549091011548365988428883E+00, \ 36.1206847744848230563063287408E+00, \ 38.7321434429335821456260416077E+00, \ 41.4518102223187411911147261814E+00, \ 44.2824730714792338393588571346E+00, \ 47.2271497842956868989350952315E+00, \ 50.2891122642406957617490218394E+00, \ 53.4719144567886528083482806195E+00, \ 56.7794246363420622130997810571E+00, \ 60.2158629090198628864175501144E+00, \ 63.7858450042359746317011396018E+00, \ 67.4944337022938858303743256950E+00, \ 71.3471996042952662866548033761E+00, \ 75.3502934256532342542905047443E+00, \ 79.5105326299863091495553913548E+00, \ 83.8355060808722578433398176585E+00, \ 88.3337015703543690861127663265E+00, \ 93.0146627285585474053033990371E+00, \ 97.8891841475781400433867276771E+00, \ 102.969556907413816507839527468E+00, \ 108.269881619615953922263509672E+00, \ 113.806473502874627389344859559E+00, \ 119.598395388304586669624529633E+00, \ 125.668172558561194312911963033E+00, \ 132.042772720911657465855905830E+00, \ 138.754984181037890781675905675E+00, \ 145.845413183135403582839942484E+00, \ 153.365484594978636237108159627E+00, \ 161.382151948137612435621726696E+00, \ 169.985706006658394387951753012E+00, \ 179.303662474015809102518278585E+00, \ 189.527895965324754736687213330E+00, \ 200.975211599246567416286718410E+00, \ 214.253685366387886426980562964E+00, \ 230.934657470897039712465629851E+00 ] ) w = np.array ( [ \ 0.0571186332138689798115872833905E+00, \ 0.120674760906403952833199320363E+00, \ 0.159250010965818737238705610965E+00, \ 0.168751783275607992345961929636E+00, \ 0.153666419776689566961937113101E+00, \ 0.123687706147164816410866522619E+00, \ 0.0892750988548486715452791500574E+00, \ 0.0582584854461059449575718257252E+00, \ 0.0345466575459925808747170858125E+00, \ 0.0186756859857146567982865525912E+00, \ 0.00922334490440935365284900752416E+00, \ 0.00416712506848395927625826634702E+00, \ 0.0017238120299900582715386728542E+00, \ 0.00065320845029716311169340559359E+00, \ 0.000226776446709095869524051732075E+00, \ 0.0000721276741548106684107502702349E+00, \ 0.0000210112611804664845988115368512E+00, \ 5.60355008933572127491815360713E-06, \ 1.3673642785604888017836641282E-06, \ 3.050726393019581724073609719E-07, \ 6.21800618393097635599817754E-08, \ 1.1566529551931711260022449E-08, \ 1.9614588267565478081534782E-09, \ 3.028617119570941124433476E-10, \ 4.252134453940068676901296E-11, \ 5.42022205780738193346988E-12, \ 6.2627306838597672554167E-13, \ 6.5474443156573322992307E-14, \ 6.18155758087291818463E-15, \ 5.259272136350738140426E-16, \ 4.023092009264648401539E-17, \ 2.7600740511819536505E-18, \ 1.69369467569682960533E-19, \ 9.2689146872177087315E-21, \ 4.509373906036563294E-22, \ 1.9435162876132376574E-23, \ 7.392627089516920704E-25, \ 2.471436415443463262E-26, \ 7.228864944674159766E-28, \ 1.840761729261403936E-29, \ 4.058349856684196011E-31, \ 7.70004964164383681E-33, \ 1.248850576499933433E-34, \ 1.71850002267670107E-36, \ 1.989637263667239694E-38, \ 1.919967137880405827E-40, \ 1.527858828552216692E-42, \ 9.9054752688842143E-45, \ 5.159752367302921188E-47, \ 2.124984666408411125E-49, \ 6.790385276685291059E-52, \ 1.6466654148296177468E-54, \ 2.9509065402691055027E-57, \ 3.78384206475710519849E-60, \ 3.33581300685424318782E-63, \ 1.922346102227388098136E-66, \ 6.781269696108301687278E-70, \ 1.34047528024406046076205E-73, \ 1.3109745101805029757648E-77, \ 5.262486388140178738869458E-82, \ 6.3780013856587414257760666E-87, \ 1.299707894237292456634747392E-92, \ 1.00085114969687540634437401684E-99 ] ) elif ( n == 64 ): x = np.array ( [ \ 0.0224158741467052800228118848190E+00, \ 0.118122512096770479797466436710E+00, \ 0.290365744018036483999130066385E+00, \ 0.539286221227979039318144947812E+00, \ 0.865037004648113944619955074710E+00, \ 1.26781404077524139811570887769E+00, \ 1.74785962605943625282996395129E+00, \ 2.30546373930750871854807054389E+00, \ 2.94096515672525184067946815211E+00, \ 3.65475265020729052703539791209E+00, \ 4.44726634331309435674255098016E+00, \ 5.31899925449639034352210985919E+00, \ 6.27049904692365391291106464633E+00, \ 7.30237000258739574722349840952E+00, \ 8.41527523948302419449521859120E+00, \ 9.60993919279610803576288204955E+00, \ 10.8871503838863721425945504202E+00, \ 12.2477645042443016181623692907E+00, \ 13.6927078455475051527299325746E+00, \ 15.2229811115247288480082687834E+00, \ 16.8396636526487372105288380392E+00, \ 18.5439181708591905236196259711E+00, \ 20.3369959487302355011498158064E+00, \ 22.2202426659508765399221543471E+00, \ 24.1951048759332539898864438802E+00, \ 26.2631372271184857851260239548E+00, \ 28.4260105275010272994997715268E+00, \ 30.6855207675259717710485823984E+00, \ 33.0435992364378291255202106805E+00, \ 35.5023238911412095869787785351E+00, \ 38.0639321656464682603573179150E+00, \ 40.7308354444586263657318695132E+00, \ 43.5056354664215298527031849317E+00, \ 46.3911429786161920736053999424E+00, \ 49.3903990256246866792358008227E+00, \ 52.5066993413463016501792769805E+00, \ 55.7436224132783804633357112912E+00, \ 59.1050619190171066088487420918E+00, \ 62.5952644001513955960550179012E+00, \ 66.2188732512475643822137626710E+00, \ 69.9809803771468292285346579722E+00, \ 73.8871872324829632109574031135E+00, \ 77.9436774344631203136879758706E+00, \ 82.1573037783193042951958683422E+00, \ 86.5356933494565182102162783753E+00, \ 91.0873756131330901456367153493E+00, \ 95.8219400155207320947672154365E+00, \ 100.750231969513979629259261451E+00, \ 105.884599468799949356360427851E+00, \ 111.239207524439582063484736638E+00, \ 116.830445051306498463386669077E+00, \ 122.677460268538576577419690565E+00, \ 128.802878769237672512753623054E+00, \ 135.233787949525827833980498879E+00, \ 142.003121489931519025140038291E+00, \ 149.151665900049388587293462932E+00, \ 156.731075132671161233616960814E+00, \ 164.808602655150522993190109025E+00, \ 173.474946836424274522152844867E+00, \ 182.858204691431463646342794510E+00, \ 193.151136037072911479385527417E+00, \ 204.672028485059455949064433343E+00, \ 218.031851935328516332452384448E+00, \ 234.809579171326164713055529725E+00 ] ) w = np.array ( [ \ 0.0562528423390298457410218545063E+00, \ 0.119023987312426027814903505889E+00, \ 0.157496403862144523820196434706E+00, \ 0.167547050415773947880904411659E+00, \ 0.153352855779236618085454792564E+00, \ 0.124221053609329744512613782193E+00, \ 0.0903423009864850577389741092016E+00, \ 0.0594777557683550242122469974397E+00, \ 0.0356275189040360718541657353369E+00, \ 0.0194804104311664060433373802715E+00, \ 0.00974359489938200224010796027138E+00, \ 0.00446431036416627529236482419054E+00, \ 0.00187535958132311482675012822252E+00, \ 0.000722646981575005122719108706619E+00, \ 0.00025548753283349670971444840218E+00, \ 0.0000828714353439694217906322403988E+00, \ 0.0000246568639678855874597337022172E+00, \ 6.7267138788296685276125455363E-06, \ 1.6817853699640888978212010865E-06, \ 3.850812981546684414827886111E-07, \ 8.06872804099049979041511092E-08, \ 1.54572370675768882800370393E-08, \ 2.7044801476174814099886074E-09, \ 4.316775475427200912314164E-10, \ 6.27775254176145220165296E-11, \ 8.30631737628895806387893E-12, \ 9.9840317872201640558973E-13, \ 1.0883538871166626853261E-13, \ 1.0740174034415901864828E-14, \ 9.57573723157444210559E-16, \ 7.69702802364858609886E-17, \ 5.56488113745402536653E-18, \ 3.6097564090104464983E-19, \ 2.0950953695489462348E-20, \ 1.0847933010975493612E-21, \ 4.994699486363804116E-23, \ 2.037836974598822311E-24, \ 7.339537564278837039E-26, \ 2.323783082198694261E-27, \ 6.43823470690876242E-29, \ 1.553121095788275271E-30, \ 3.24425009201953731E-32, \ 5.8323862678362015E-34, \ 8.96325483310285406E-36, \ 1.168703989550736241E-37, \ 1.282055984359980381E-39, \ 1.172094937405002292E-41, \ 8.83533967232860498E-44, \ 5.42495559030618659E-46, \ 2.675542666678893829E-48, \ 1.042917031411367078E-50, \ 3.152902351957772624E-53, \ 7.22954191064752234E-56, \ 1.2242353012300822645E-58, \ 1.48216850490191041178E-61, \ 1.23251934881451880806E-64, \ 6.69149900457126952681E-68, \ 2.220465941850448995507E-71, \ 4.1209460947388762499791E-75, \ 3.77439906189648917041762E-79, \ 1.414115052917619417463147E-83, \ 1.5918330640413679178610318E-88, \ 2.98948434886063430774131269E-94, \ 2.0890635084369527708281542544E-101 ] ) elif ( n == 65 ): x = np.array ( [ \ 0.0220736343882500875264595737093E+00, \ 0.116318612213376151729622328698E+00, \ 0.285929513070813951834551909860E+00, \ 0.531041775784488438911664842933E+00, \ 0.851801670809046586655299989571E+00, \ 1.24839628201831707727195703687E+00, \ 1.72105687981755734816623923359E+00, \ 2.27006018491690256109784837001E+00, \ 2.89572940756799471192249006458E+00, \ 3.59843535756478540694788870796E+00, \ 4.37859769744118464804519621154E+00, \ 5.23668636694320050319815958793E+00, \ 6.17322319658730631921440545744E+00, \ 7.18878372629467202131889616235E+00, \ 8.28399924588871831467573911308E+00, \ 9.45955907610065448076092041454E+00, \ 10.7162131111897048393914349801E+00, \ 12.0547746472322707150580323735E+00, \ 13.4761235235671154056092903386E+00, \ 14.9812096088541520753799758172E+00, \ 16.5710566677964491577962746244E+00, \ 18.2467666498987672118974219097E+00, \ 20.0095244478287060731090711532E+00, \ 21.8606031801774165914390699117E+00, \ 23.8013700618933285635853631176E+00, \ 25.8332929356397220962712840077E+00, \ 27.9579475491204073878989540109E+00, \ 30.1770256774182582795717815112E+00, \ 32.4923442060863420003362903722E+00, \ 34.9058553107319841822666865568E+00, \ 37.4196578929107315489849223258E+00, \ 40.0360104612770088389674875188E+00, \ 42.7573456823686148915804841094E+00, \ 45.5862868687358177811114530444E+00, \ 48.5256667254367437021219033875E+00, \ 51.5785487419130140104165726852E+00, \ 54.7482516984863756567192528045E+00, \ 58.0383778598867354584946224426E+00, \ 61.4528455586293273580430507845E+00, \ 64.9959270371996369214889214525E+00, \ 68.6722926314626183977917033408E+00, \ 72.4870626544527259157609330997E+00, \ 76.4458687019847672439750100021E+00, \ 80.5549265807842719390299008467E+00, \ 84.8211237010524840445780520727E+00, \ 89.2521246438779093867045988317E+00, \ 93.8564998060605244752886814683E+00, \ 98.6438836854008198627513004124E+00, \ 103.625171719648548339736534290E+00, \ 108.812767977808831403825388295E+00, \ 114.220900975902615729136419234E+00, \ 119.866032356536657109576887729E+00, \ 125.767394661236316522917056970E+00, \ 131.947712599442095787498603776E+00, \ 138.434191890473005752666966171E+00, \ 145.259909991527292147157412636E+00, \ 152.465831757831086161761248192E+00, \ 160.103837850755827943698932303E+00, \ 168.241478626055331550636477652E+00, \ 176.969855979856624954098184957E+00, \ 186.417642483351089954653964415E+00, \ 196.778474440876949259615139650E+00, \ 208.372107380940491095442543113E+00, \ 221.812376576320945562507410640E+00, \ 238.685811594674270102373709659E+00 ] ) w = np.array ( [ \ 0.0554129011565536469555170462551E+00, \ 0.117417396564162014386769936525E+00, \ 0.15577793159527363526750345236E+00, \ 0.166347955884031811873697185854E+00, \ 0.153013207065446887512281359026E+00, \ 0.12471061536737329712442529837E+00, \ 0.0913671486268474804579363734334E+00, \ 0.0606693673532322224974724445698E+00, \ 0.0366985078337756899608575633553E+00, \ 0.0202884358923229233158787730215E+00, \ 0.0102732022687699783894639990081E+00, \ 0.00477128781081110626106879095602E+00, \ 0.00203437021965744474885076853755E+00, \ 0.00079674216708789273511811886929E+00, \ 0.000286683812097562728436084278246E+00, \ 0.0000947743836779584423250711498309E+00, \ 0.0000287808776386491122522878225936E+00, \ 8.025921887785674361327140519E-06, \ 2.0542534210210521080625753887E-06, \ 4.822974163227069271800228998E-07, \ 1.037906330975825689484858253E-07, \ 2.04556458252437904249066042E-08, \ 3.6885834829334325209249956E-09, \ 6.07893150020096839531226E-10, \ 9.14524981574057744811517E-11, \ 1.25427414380884616209197E-11, \ 1.56600212784699337922365E-12, \ 1.7771074191193507379193E-13, \ 1.829851898040443279934E-14, \ 1.70645929547049792703E-15, \ 1.438412537484673440005E-16, \ 1.09354404172789017674E-17, \ 7.4805627565827998507E-19, \ 4.5927490046001844919E-20, \ 2.5237976161210732972E-21, \ 1.2376030276622370811E-22, \ 5.398129612170324038E-24, \ 2.086925656272980914E-25, \ 7.12363601216912351E-27, \ 2.13797949495352507E-28, \ 5.61585996656691837E-30, \ 1.2845455347843963E-31, \ 2.5444410680246895E-33, \ 4.33793017530204526E-35, \ 6.3222072485073684E-37, \ 7.8174607001716233E-39, \ 8.1320382378781478E-41, \ 7.0491916339430245E-43, \ 5.03749289878460876E-45, \ 2.93162035252999008E-47, \ 1.370002490040754814E-49, \ 5.05827802154356236E-52, \ 1.447822639997111427E-54, \ 3.141466864703300069E-57, \ 5.03056294905086669E-60, \ 5.7547901892214244076E-63, \ 4.5172924325696051375E-66, \ 2.31224468889972999556E-69, \ 7.22311071834335770012E-73, \ 1.2595483022441380495635E-76, \ 1.08123622593537779961256E-80, \ 3.78397004144107162756714E-85, \ 3.9595563374024690284872814E-90, \ 6.85929105947869810086088696E-96, \ 4.3543678721167358517710196959E-103 ] ) elif ( n == 127 ): x = np.array ( [ \ 0.0113396352985186116918931696313E+00, \ 0.0597497534357266202813482370574E+00, \ 0.146850986907461676123882236874E+00, \ 0.272675907358595531313780082789E+00, \ 0.437246006441926655545770358699E+00, \ 0.640586882225669295335764164000E+00, \ 0.882729686390583644814876536500E+00, \ 1.16371141601665376615605847010E+00, \ 1.48357501528346138913135848610E+00, \ 1.84236943516135653806863208099E+00, \ 2.24014968395790242445133156565E+00, \ 2.67697687801413036921678699612E+00, \ 3.15291829570828255657715083088E+00, \ 3.66804743603047525402263399265E+00, \ 4.22244408233018884559778766674E+00, \ 4.81619437158705024756655350873E+00, \ 5.44939086945594167558621789084E+00, \ 6.12213265129972541939445847632E+00, \ 6.83452538941226681122379949733E+00, \ 7.58668144663674721742059868368E+00, \ 8.37871997659327252548421206595E+00, \ 9.21076703074265587779225061024E+00, \ 10.0829556725286438091664393536E+00, \ 10.9954260988581254298031473588E+00, \ 11.9483257691977259976106051279E+00, \ 12.9418095425855310537233810982E+00, \ 13.9760398228785065200144056687E+00, \ 15.0511867125795236315747963654E+00, \ 16.1674281756128529229773950518E+00, \ 17.3249502094436734465611637126E+00, \ 18.5239470269656885608117113093E+00, \ 19.7646212486115041040716693869E+00, \ 21.0471841051731836068770440201E+00, \ 22.3718556518555428176481239181E+00, \ 23.7388649941224971836523137887E+00, \ 25.1484505259373682340772783856E+00, \ 26.6008601810417496072533842798E+00, \ 28.0963516979646192017539612921E+00, \ 29.6351928995041789106102271386E+00, \ 31.2176619874797591442144671526E+00, \ 32.8440478536104304605229513413E+00, \ 34.5146504074411491491056359474E+00, \ 36.2297809223068040196153885089E+00, \ 37.9897624003999564359687801403E+00, \ 39.7949299580899617783964371417E+00, \ 41.6456312327301807051539908975E+00, \ 43.5422268122868595499508929938E+00, \ 45.4850906892287911379961513367E+00, \ 47.4746107402319647194687665991E+00, \ 49.5111892333790877167288845844E+00, \ 51.5952433646712444431827712669E+00, \ 53.7272058258193167582881400691E+00, \ 55.9075254054475533058306059917E+00, \ 58.1366676260224391970775260257E+00, \ 60.4151154190185902957071920538E+00, \ 62.7433698410518097002071267427E+00, \ 65.1219508339499963119560254171E+00, \ 67.5513980319978863144118724431E+00, \ 70.0322716198845845112298711920E+00, \ 72.5651532452068490908886694168E+00, \ 75.1506469897399352993543623251E+00, \ 77.7893804040858160006474054621E+00, \ 80.4820056107507292058039629268E+00, \ 83.2292004811959148867961200190E+00, \ 86.0316698929535829667982387326E+00, \ 88.8901470735120510996525185443E+00, \ 91.8053950383581779949712501705E+00, \ 94.7782081313315832053870310348E+00, \ 97.8094136763051164110541101154E+00, \ 100.899873750172859403719397622E+00, \ 104.050487088215989347040768450E+00, \ 107.262191134146004284231164014E+00, \ 110.535964248515005306027713513E+00, \ 113.872828090758394853483761877E+00, \ 117.273850191925177740954778864E+00, \ 120.740146737188801061739780027E+00, \ 124.272885579556983542595064469E+00, \ 127.873289508859426450938417454E+00, \ 131.542639803143669218093777421E+00, \ 135.282280093118369701327381064E+00, \ 139.093620574329700139644220870E+00, \ 142.978142606436017768082277536E+00, \ 146.937403744373665494410809691E+00, \ 150.973043252521871274925114375E+00, \ 155.086788160346125722296414206E+00, \ 159.280459926632882354019569899E+00, \ 163.555981789575711040159671821E+00, \ 167.915386891943601342455471847E+00, \ 172.360827284738125368381561917E+00, \ 176.894583929601921763116749935E+00, \ 181.519077840368130692275288340E+00, \ 186.236882528281123738612025304E+00, \ 191.050737944509291967908366108E+00, \ 195.963566148798798378390025430E+00, \ 200.978488976000251536964755261E+00, \ 206.098848024688711121272830428E+00, \ 211.328227356716552605723772570E+00, \ 216.670479376582303234770894658E+00, \ 222.129754459296872462673049638E+00, \ 227.710535020722324190891324313E+00, \ 233.417674882826024533677753226E+00, \ 239.256444988303086200187496671E+00, \ 245.232586778715671725312540190E+00, \ 251.352374887181280300055009918E+00, \ 257.622691237920614130761918823E+00, \ 264.051113229082405517543772418E+00, \ 270.646019457227967492991117186E+00, \ 277.416717501636510717983882181E+00, \ 284.373599742208703266744028731E+00, \ 291.528335213464957195812820216E+00, \ 298.894108370282486008788956154E+00, \ 306.485919782626113204181124239E+00, \ 314.320969864711774874000075076E+00, \ 322.419155891286796833494403613E+00, \ 330.803726638024056519338473349E+00, \ 339.502161278324337477353675960E+00, \ 348.547375594726973554807617874E+00, \ 357.979420280298454540490074431E+00, \ 367.847945200760045788583414229E+00, \ 378.215906231355328183329791889E+00, \ 389.165391412510041015794753252E+00, \ 400.807293314517025899963612864E+00, \ 413.298536817793844180082600819E+00, \ 426.875791536636755382885090171E+00, \ 441.930854853108414124603092718E+00, \ 459.218046398884299819712673132E+00, \ 480.693782633883738597042692293E+00 ] ) w = np.array ( [ \ 0.0287732466920001243557700103008E+00, \ 0.0638174681751346493634809492651E+00, \ 0.0919196697215705713898641946531E+00, \ 0.11054167914413766381245463003E+00, \ 0.118797716333758501883283294227E+00, \ 0.117378185300526951488044516301E+00, \ 0.108193059841805514883351455812E+00, \ 0.0938270752904896280803772614011E+00, \ 0.0769664509605888439958224859284E+00, \ 0.0599349039129397143325707300635E+00, \ 0.0444177420738890013717083162729E+00, \ 0.0313850809662523209830093722151E+00, \ 0.021172316041924506411370709025E+00, \ 0.0136501453642305416521711855646E+00, \ 0.00841728527105991722793666573854E+00, \ 0.00496749900598827605159128586202E+00, \ 0.00280699038950018846319619574464E+00, \ 0.00151929510039419524604453410578E+00, \ 0.000787890287517960840862172871405E+00, \ 0.00039156751064868450584507324649E+00, \ 0.000186524342688258605500935662601E+00, \ 0.0000851731604155766219088098281602E+00, \ 0.0000372856391978530377121453215777E+00, \ 0.0000156484167917129939474478052968E+00, \ 6.2964340695224829035692735525E-06, \ 2.42889297113287245745413799382E-06, \ 8.9824607890051007201922871545E-07, \ 3.18441747407603537107429663281E-07, \ 1.08212729055668392118618075427E-07, \ 3.52450767506355360159027790853E-08, \ 1.10012243657193474070638397617E-08, \ 3.29040796167179321253293430033E-09, \ 9.4289145237889976419772700773E-10, \ 2.58825789046683181840501953093E-10, \ 6.80474371033707626309422590176E-11, \ 1.71313988051208378353995644756E-11, \ 4.12917445240528654694439223049E-12, \ 9.52641897188072732207076648735E-13, \ 2.10326044324424259329629420475E-13, \ 4.44271519387293528609404342858E-14, \ 8.97605003628337033233198464055E-15, \ 1.73415114077692870746279483468E-15, \ 3.20280995489883566314943798352E-16, \ 5.65313889507936820226607420952E-17, \ 9.53296727990265912345880440259E-18, \ 1.53534534773101425652885094376E-18, \ 2.36089621794673656860578421322E-19, \ 3.46487427944566113321938766532E-20, \ 4.85152418970864613201269576635E-21, \ 6.47862286335198134281373737907E-22, \ 8.2476020965403242936448553126E-23, \ 1.0005361880214719793491658283E-23, \ 1.1561395116207304954233181264E-24, \ 1.271934273116792265561213426E-25, \ 1.331658471416537296734000416E-26, \ 1.32612184546789440336461085E-27, \ 1.25549954476439498072860741E-28, \ 1.1294412178579462703240913E-29, \ 9.649102027956211922850061E-31, \ 7.82418467683020993967331E-32, \ 6.01815035422196266582499E-33, \ 4.38824827049617415515105E-34, \ 3.0314137647517256304036E-35, \ 1.9826016543944539545225E-36, \ 1.2267623373665926559014E-37, \ 7.176393169250888894381E-39, \ 3.965937883383696358411E-40, \ 2.068897055386804009958E-41, \ 1.017958701797951724527E-42, \ 4.72008277459863746257E-44, \ 2.06068289855533748257E-45, \ 8.4627575907305987246E-47, \ 3.2661123687088798658E-48, \ 1.1833939207883162381E-49, \ 4.021120912389501381E-51, \ 1.2799824394111125389E-52, \ 3.81238777475488465E-54, \ 1.061205754270115677E-55, \ 2.757144694720040359E-57, \ 6.67725442409284929E-59, \ 1.505243838386823495E-60, \ 3.15389868001137585E-62, \ 6.13266142994831808E-64, \ 1.10485100303248106E-65, \ 1.84105635380913481E-67, \ 2.83239265700528322E-69, \ 4.01544098437636555E-71, \ 5.23515302156837088E-73, \ 6.2634476665005101E-75, \ 6.861221053566653E-77, \ 6.8651298840956019E-79, \ 6.25813884337280849E-81, \ 5.1833271237514904E-83, \ 3.88936215719184435E-85, \ 2.63577113794769328E-87, \ 1.60788512939179797E-89, \ 8.79780420709689396E-92, \ 4.30134050774951099E-94, \ 1.871343588134283853E-96, \ 7.212574470806047168E-99, \ 2.450874606217787438E-101, \ 7.304209461947087578E-104, \ 1.8983290818383463538E-106, \ 4.2757400244246684123E-109, \ 8.2894681420515755691E-112, \ 1.37294322193244000131E-114, \ 1.926546412640497322204E-117, \ 2.269334450330135482614E-120, \ 2.2209290603717355061909E-123, \ 1.7851087685544512662857E-126, \ 1.16309319903871644674312E-129, \ 6.05244435846523922909528E-133, \ 2.472956911506352864762838E-136, \ 7.778906500648941036499721E-140, \ 1.8409738662712607039570678E-143, \ 3.1900921131079114970179072E-147, \ 3.917948713917419973761766608E-151, \ 3.2782158394188697053774429821E-155, \ 1.77935907131388880628196401287E-159, \ 5.88823534089326231574678353812E-164, \ 1.09572365090711698777472032739E-168, \ 1.02816211148670008982850769758E-173, \ 4.1704725557697758145816510854E-179, \ 5.8002877720316101774638319602E-185, \ 1.88735077458255171061716191011E-191, \ 6.91066018267309116827867059509E-199, \ 4.35068132011058556283833133344E-208 ] ) elif ( n == 128 ): x = np.array ( [ \ 0.0112513882636759629608518403162E+00, \ 0.0592847412690264542879220089614E+00, \ 0.145707966594312465141854059102E+00, \ 0.270553178758665066190760897100E+00, \ 0.433841407553836803056096580754E+00, \ 0.635597665781621938340867677969E+00, \ 0.875852384546520779155346013261E+00, \ 1.15464170197439795008153355708E+00, \ 1.47200756316673547554446633038E+00, \ 1.82799777831235028535984528718E+00, \ 2.22266607156190244817896452914E+00, \ 2.65607212988348119522885329309E+00, \ 3.12828165502791695498310369738E+00, \ 3.63936641985240321221074522169E+00, \ 4.18940432959404797478493079865E+00, \ 4.77847948843487609165724239213E+00, \ 5.40668227160049918527893820105E+00, \ 6.07410940319653684309155844506E+00, \ 6.78086403997562541104804929943E+00, \ 7.52705586122937588585512279842E+00, \ 8.31280116500777060337884381191E+00, \ 9.13822297088039239600262641969E+00, \ 10.0034511294682220892682761435E+00, \ 10.9086224389908825478488613010E+00, \ 11.8538807690918568038332644538E+00, \ 12.8393771922232496874551935673E+00, \ 13.8652701228920803029536799971E+00, \ 14.9317254650919274737473553133E+00, \ 16.0389167682670793509213783428E+00, \ 17.1870253921812651027585044591E+00, \ 18.3762406810896949333827523370E+00, \ 19.6067601476416467279054690989E+00, \ 20.8787896669713729158932014403E+00, \ 22.1925436814678369066763923182E+00, \ 23.5482454167489205609249730097E+00, \ 24.9461271094034886279510396640E+00, \ 26.3864302471052908976269305132E+00, \ 27.8694058217463902295696818564E+00, \ 29.3953145962849137215656288381E+00, \ 30.9644273860527540023220861317E+00, \ 32.5770253553237501781419486456E+00, \ 34.2334003300022426604794108753E+00, \ 35.9338551273561538107722924963E+00, \ 37.6787039037883744300655582016E+00, \ 39.4682725217157641271489033004E+00, \ 41.3028989367070896380080417637E+00, \ 43.1829336061203832438783635225E+00, \ 45.1087399205772317441506148507E+00, \ 47.0806946597172168560725351128E+00, \ 49.0991884737910268021535852860E+00, \ 51.1646263927766594446404335916E+00, \ 53.2774283648407739161085367944E+00, \ 55.4380298261178918683089638291E+00, \ 57.6468823039452288144249811220E+00, \ 59.9044540558720556965292635062E+00, \ 62.2112307469614582456791552962E+00, \ 64.5677161681212154290410515467E+00, \ 66.9744329984415610548027156195E+00, \ 69.4319236147834299557621097742E+00, \ 71.9407509521543751573018481062E+00, \ 74.5014994187340277930279831855E+00, \ 77.1147758697705705283198924354E+00, \ 79.7812106449685528544582124991E+00, \ 82.5014586744314529140391768845E+00, \ 85.2762006587153587377964042582E+00, \ 88.1061443290995036940317393258E+00, \ 90.9920257947926131560303030245E+00, \ 93.9346109844796944955244642925E+00, \ 96.9346971903819404516199551240E+00, \ 99.9931147238642715216213000267E+00, \ 103.110728692593987392319749158E+00, \ 106.288440910345442668426129659E+00, \ 109.527191951777550806618056918E+00, \ 112.827963365904193877333487264E+00, \ 116.191780063556780940235871708E+00, \ 119.619712895932010462348887420E+00, \ 123.112881443360190060911814509E+00, \ 126.672457035760183662338694957E+00, \ 130.299666028913462587217492864E+00, \ 133.995793363747964343582120836E+00, \ 137.762186439339380964302666578E+00, \ 141.600259334393040305789642722E+00, \ 145.511497416659592393640597008E+00, \ 149.497462385177707088173175451E+00, \ 153.559797796566440117982748261E+00, \ 157.700235133978105059095336546E+00, \ 161.920600485975634163753629031E+00, \ 166.222821912768875092875739160E+00, \ 170.608937589242234646550663310E+00, \ 175.081104828414604880617405502E+00, \ 179.641610105866994602634964639E+00, \ 184.292880225846805341834505020E+00, \ 189.037494793954109001292998345E+00, \ 193.878200190472967540802875940E+00, \ 198.817925273720602804745944994E+00, \ 203.859799085769844571664824897E+00, \ 209.007170885510867853387511181E+00, \ 214.263632898788021280527758492E+00, \ 219.633046255578174038387401024E+00, \ 225.119570684209027756659796566E+00, \ 230.727698658203619681658868680E+00, \ 236.462294850177665966018904158E+00, \ 242.328641949702698267864519866E+00, \ 248.332494162357178892016601780E+00, \ 254.480140044869131893543803358E+00, \ 260.778476773579736538560064538E+00, \ 267.235098528953836763992472029E+00, \ 273.858402462693609793414602648E+00, \ 280.657716776323492397504100977E+00, \ 287.643456899219330638473677900E+00, \ 294.827317787647739179806672104E+00, \ 302.222513246449465380535981711E+00, \ 309.844077326612663447772363643E+00, \ 317.709248954906289495678052340E+00, \ 325.837970121194949650401277931E+00, \ 334.253542067654135375184450174E+00, \ 342.983506273825316408508913329E+00, \ 352.060853546526185083043426984E+00, \ 361.525726392325047599066851839E+00, \ 371.427889214327523078517984867E+00, \ 381.830444119061080196207616882E+00, \ 392.815671240808098809377819898E+00, \ 404.494724750515074389666071660E+00, \ 417.024902977989015820197277594E+00, \ 430.643444166597381558323551668E+00, \ 445.743096973927989652171720726E+00, \ 463.080034109446258208013793406E+00, \ 484.615543986443976044063131110E+00 ] ) w = np.array ( [ \ 0.0285518444532397286290731773612E+00, \ 0.0633502117845051187797978127259E+00, \ 0.0913083813661343144231616325903E+00, \ 0.109913900410911746101013915833E+00, \ 0.118274171034173698789809688874E+00, \ 0.117045739000406721566458439207E+00, \ 0.108089987545568415436473783125E+00, \ 0.0939428886389285017878088436356E+00, \ 0.0772536687978980532077800252359E+00, \ 0.0603270562656615705389303086003E+00, \ 0.0448473482471952140682424657998E+00, \ 0.0317969479368768461739632484821E+00, \ 0.0215301494537944439261107285438E+00, \ 0.0139369517338463483277576885975E+00, \ 0.00863158538020224714884473096489E+00, \ 0.00511777701366922852873936722845E+00, \ 0.00290634743648595585817980077219E+00, \ 0.00158143294331667939723416013489E+00, \ 0.000824738985098812150435438593253E+00, \ 0.000412326088539694730970290830804E+00, \ 0.000197649426442591498620529889783E+00, \ 0.0000908515788782451508022826306153E+00, \ 0.0000400484927835805298977887660442E+00, \ 0.0000169307623980817855755102888475E+00, \ 6.86452529111068208938636278412E-06, \ 2.66921659814210266015872228584E-06, \ 9.95364010286384477177483332196E-07, \ 3.55943575300306543988020166563E-07, \ 1.22053255194881194831205615734E-07, \ 4.01279192093563506890167766024E-08, \ 1.26481141474759786445650110908E-08, \ 3.82148972942657229023411372003E-09, \ 1.10664105922734169994480044024E-09, \ 3.07100923709742319582290034639E-10, \ 8.16549938415448956026437885004E-11, \ 2.07985363278137784234189612116E-11, \ 5.0739537708398704043296986402E-12, \ 1.1853143771796112305093733131E-12, \ 2.65092752372887358600565488195E-13, \ 5.67463221575765876681065606161E-14, \ 1.16237381470751589221529434901E-14, \ 2.27776629270238637919733104451E-15, \ 4.26883197029764927739172104126E-16, \ 7.64928879936327510525948457803E-17, \ 1.31013139198382464188082886821E-17, \ 2.1441452341246636343706788692E-18, \ 3.35194428720884780801470729044E-19, \ 5.00373308645947376823179365121E-20, \ 7.13003064195856212049702464626E-21, \ 9.6945407403972664035320905829E-22, \ 1.25728475563978459844059927432E-22, \ 1.5546610955630634482202731199E-23, \ 1.832109793253421778719084254E-24, \ 2.056797978136734920722781372E-25, \ 2.19866605262329119257657449E-26, \ 2.23691600732428936729406222E-27, \ 2.1649606446339054400256309E-28, \ 1.9922276806187937873877251E-29, \ 1.742153886325439585907653E-30, \ 1.446949786106284637699605E-31, \ 1.1407517061230822834189E-32, \ 8.5318050978102090722116E-34, \ 6.04970117793885843505E-35, \ 4.0643432432648003017795E-36, \ 2.585349374987909630703E-37, \ 1.556028762522623447585E-38, \ 8.85462584966333001103E-40, \ 4.76045751736458068032E-41, \ 2.416078510661232205E-42, \ 1.15664705033873749321E-43, \ 5.2185106194923759952E-45, \ 2.2169743353361803305E-46, \ 8.86010275661369606E-48, \ 3.327811159201095553E-49, \ 1.173490043078302544E-50, \ 3.880967726420921431E-52, \ 1.202426327933061418E-53, \ 3.48602304410554638E-55, \ 9.44554522159556681E-57, \ 2.38888427455968395E-58, \ 5.63188475075463052E-60, \ 1.23592861191216019E-61, \ 2.52100420237726743E-63, \ 4.7722246219998052E-65, \ 8.3700198919995783E-67, \ 1.35782434112020985E-68, \ 2.03368872715315416E-70, \ 2.8068384806953538E-72, \ 3.562567607062096E-74, \ 4.1494527492937706E-76, \ 4.4250079657663219E-78, \ 4.3100842612898497E-80, \ 3.8246610167617398E-82, \ 3.08354784259879275E-84, \ 2.25213982217062084E-86, \ 1.48551474064504312E-88, \ 8.8196354763726564E-91, \ 4.69641782212598507E-93, \ 2.23439382545477274E-95, \ 9.45878703822074032E-98, \ 3.546960831240672614E-100, \ 1.17253213003488723E-102, \ 3.399090555639915548E-105, \ 8.591907200623898045E-108, \ 1.8818913973535359647E-110, \ 3.5473586323062565237E-113, \ 5.7114822282836004745E-116, \ 7.78947378804446095611E-119, \ 8.91589869949126935148E-122, \ 8.476856358868403207418E-125, \ 6.617326935494900345408E-128, \ 4.1862163574157095190077E-131, \ 2.11438516898114207120093E-134, \ 8.38216350136786953641675E-138, \ 2.557202302197677884687798E-141, \ 5.8667686421912043720461236E-145, \ 9.8498610300648438019885689E-149, \ 1.171383943342068942456857274E-152, \ 9.483963265567383663821702301E-157, \ 4.9770963811238028116653976343E-161, \ 1.59089852775099765481980638695E-165, \ 2.85630382911900292320607568044E-170, \ 2.58225071969148999265031459122E-175, \ 1.00735025005079740952983187255E-180, \ 1.34425250044381631821772983363E-186, \ 4.18296221403683473389726627221E-193, \ 1.45716530772618631594481663188E-200, \ 8.64059169046870867692891422354E-210 ] ) elif ( n == 129 ): x = np.array ( [ \ 0.0111645041367687260935881187114E+00, \ 0.0588269115255121725669144777376E+00, \ 0.144582603939087375345544455104E+00, \ 0.268463250498790809142537571727E+00, \ 0.430489433028069665583513882755E+00, \ 0.630685596971157529700818698614E+00, \ 0.869081474989540465988995980646E+00, \ 1.14571237269034129786358037349E+00, \ 1.46061926689785560022252086358E+00, \ 1.81384886225287260620048305182E+00, \ 2.20545363849013952710373368048E+00, \ 2.63549189753739459262727316570E+00, \ 3.10402781353627480023526416641E+00, \ 3.61113148701933289479734007535E+00, \ 4.15687900382495881133416031205E+00, \ 4.74135249908325871733484826319E+00, \ 5.36464022650680264548807369539E+00, \ 6.02683663318167548105631862177E+00, \ 6.72804244004243132025609101021E+00, \ 7.46836472821534963467632383543E+00, \ 8.24791703142169723816558449856E+00, \ 9.06681943464370270026626900050E+00, \ 9.92519867926931734070041188408E+00, \ 10.8231882749469306495297612192E+00, \ 11.7609286183977310387181197615E+00, \ 12.7385671194512351722694605084E+00, \ 13.7562583345886271805335101149E+00, \ 14.8141641082989854857712290559E+00, \ 15.9124537225752979381236294324E+00, \ 17.0513040549004685335351914932E+00, \ 18.2308997450984136591429080617E+00, \ 19.4514333714519620150207362048E+00, \ 20.7131056365177555775299262985E+00, \ 22.0161255630988608706489924430E+00, \ 23.3607107008685190470514486749E+00, \ 24.7470873441735867407744490421E+00, \ 26.1754907615839641134296855243E+00, \ 27.6461654377949106206644801830E+00, \ 29.1593653285328756045576144321E+00, \ 30.7153541291626095441732915451E+00, \ 32.3144055577441922161871665693E+00, \ 33.9568036533435689847296719094E+00, \ 35.6428430904596160112634717165E+00, \ 37.3728295104950910213327545948E+00, \ 39.1470798712685466663878582421E+00, \ 40.9659228156399190364649448364E+00, \ 42.8296990604046437906422357564E+00, \ 44.7387618067004519884778950119E+00, \ 46.6934771732681867037686990052E+00, \ 48.6942246540138734219622380649E+00, \ 50.7413976014347803131042845818E+00, \ 52.8354037375983340937979164025E+00, \ 54.9766656945006500240481182310E+00, \ 57.1656215857823649284158070179E+00, \ 59.4027256119448606421881531943E+00, \ 61.6884487013914405461822377003E+00, \ 64.0232791898173852597210780437E+00, \ 66.4077235406921080587914699631E+00, \ 68.8423071098181639647332557636E+00, \ 71.3275749572182499453797757024E+00, \ 73.8640927098955268421782575110E+00, \ 76.4524474793379566181613942983E+00, \ 79.0932488379977030145472340597E+00, \ 81.7871298593763443093790704140E+00, \ 84.5347482267906647046323684124E+00, \ 87.3367874163878117910865422310E+00, \ 90.1939579605291478450570652459E+00, \ 93.1069987982766656767050611186E+00, \ 96.0766787204029972427806506124E+00, \ 99.1037979171157474398207782757E+00, \ 102.189189637550616978355114969E+00, \ 105.333721971058838012388514189E+00, \ 108.538299761408281119757506569E+00, \ 111.803866666252185387269569516E+00, \ 115.131407375615803792171876281E+00, \ 118.521950004733905726449958829E+00, \ 121.976568678369858697173472594E+00, \ 125.496386325793836628100280130E+00, \ 129.082577707933597477650969878E+00, \ 132.736372700883616552797038522E+00, \ 136.459059863023413416361147154E+00, \ 140.251990316520692590651584246E+00, \ 144.116581978059547282038191264E+00, \ 148.054324178334554730971189024E+00, \ 152.066782715303825347545842677E+00, \ 156.155605392537787829354492826E+00, \ 160.322528101405362530717313062E+00, \ 164.569381514511906899139962575E+00, \ 168.898098467996847713856358122E+00, \ 173.310722122324145053009369479E+00, \ 177.809415005439611927392788370E+00, \ 182.396469059102149766157602559E+00, \ 187.074316829415599837320402996E+00, \ 191.845543966839763114071401295E+00, \ 196.712903230183761859963922576E+00, \ 201.679330224475912387142876872E+00, \ 206.747961145685983577272619640E+00, \ 211.922152858007833039218477193E+00, \ 217.205505694330143211608701365E+00, \ 222.601889450939732907762241579E+00, \ 228.115473147766504188912042615E+00, \ 233.750759251359480867215068547E+00, \ 239.512623216994726852324857048E+00, \ 245.406359409276117119061170837E+00, \ 251.437734721509742305967783880E+00, \ 257.613051552607945102309836371E+00, \ 263.939222243647173894814944292E+00, \ 270.423857663083214051346532320E+00, \ 277.075373415313344577287378499E+00, \ 283.903118212107869887400929941E+00, \ 290.917530409009503510470042900E+00, \ 298.130330747241946479391511151E+00, \ 305.554762228622700877217556637E+00, \ 313.205892212538716296350101328E+00, \ 321.100997941634721519100026717E+00, \ 329.260065894410473958350680155E+00, \ 337.706449515634131989920236326E+00, \ 346.467752279350659621376501841E+00, \ 355.577039643063413893183224979E+00, \ 365.074545471124791778391196263E+00, \ 375.010148136708978052975802762E+00, \ 385.447095254054417308720464640E+00, \ 396.467858100744210106334636127E+00, \ 408.183851152492844798297769341E+00, \ 420.752744334742187498526476928E+00, \ 434.412341688764625555428748148E+00, \ 449.556338392256949417199002480E+00, \ 466.942750921706688536121321308E+00, \ 488.537715007400745716181291102E+00 ] ) w = np.array ( [ \ 0.0283338232816188129433412493366E+00, \ 0.0628897352309939992519628028429E+00, \ 0.0907050560197830441591715791845E+00, \ 0.109292734964339745013347523543E+00, \ 0.117753891824430328742552706746E+00, \ 0.116712333575132760088854393741E+00, \ 0.1079821092277907522768638822E+00, \ 0.0940513886437790878162542877426E+00, \ 0.0775328171368385256641246588694E+00, \ 0.0607119801995722871258201910352E+00, \ 0.0452716214541695196710137988047E+00, \ 0.0322057586869443933590250840601E+00, \ 0.0218870093879284288723521418152E+00, \ 0.0142243242185532561642375502974E+00, \ 0.00884734285745239479408590424342E+00, \ 0.00526983370954167607842815218011E+00, \ 0.00300740619275414763773247784756E+00, \ 0.00164498171784021535901621253553E+00, \ 0.000862641473273809069700952476134E+00, \ 0.000433807488545501081264834235514E+00, \ 0.000209234988721404556453070968853E+00, \ 0.0000968044053231071525887634259114E+00, \ 0.0000429650601010182583779356860953E+00, \ 0.0000182943298240488545326843922155E+00, \ 7.47320473307839845584026474317E-06, \ 2.92876004890558731746712968433E-06, \ 1.10111937532188602299646730309E-06, \ 3.97133727854894494886436944708E-07, \ 1.37391737873739072964678053016E-07, \ 4.55898285044463980401770363171E-08, \ 1.45082031554226827387170770004E-08, \ 4.42736861865778798052557346184E-09, \ 1.29540549841465072618582643105E-09, \ 3.63353401896969889688016611161E-10, \ 9.76889957112077658988662065766E-11, \ 2.51697359198850123687093430919E-11, \ 6.2136427115425329244941688694E-12, \ 1.46947065273427272155102255087E-12, \ 3.3283536396381226771786168693E-13, \ 7.21860543546415622515782097245E-14, \ 1.49874700296546634758941598894E-14, \ 2.97813865190408297766537928957E-15, \ 5.66223500996744709699260363288E-16, \ 1.02976110977345161229212606736E-16, \ 1.79087076765055918801501255712E-17, \ 2.97741214327584722879794953728E-18, \ 4.73066849378813640521244315218E-19, \ 7.18076704552391091114386577815E-20, \ 1.0409591754013912471892470954E-20, \ 1.44063705945958837668569771815E-21, \ 1.9027009013059586477368991424E-22, \ 2.3972421860336028068385342016E-23, \ 2.880065029076382866335001882E-24, \ 3.2980570110683255202892323E-25, \ 3.59822818119059018987046195E-26, \ 3.7384843519427824153681456E-27, \ 3.6971969670644497346136084E-28, \ 3.478607942989822329014257E-29, \ 3.112229078360896126467536E-30, \ 2.64630166366922810478446E-31, \ 2.13731385180863223984415E-32, \ 1.63873356712820982018691E-33, \ 1.1920639048111247727415E-34, \ 8.221888191494076473793E-36, \ 5.373327742595686629791E-37, \ 3.325235584661609413228E-38, \ 1.94717317556033610096E-39, \ 1.07813497736466418105E-40, \ 5.6402504582069233692E-42, \ 2.785716667292756732E-43, \ 1.2978694111929463222E-44, \ 5.699117216622829387E-46, \ 2.356556045713220169E-47, \ 9.167179452095711245E-49, \ 3.351643630271094859E-50, \ 1.15053967361148792E-51, \ 3.70428664291287775E-53, \ 1.117334474142203311E-54, \ 3.15377989811063792E-56, \ 8.319920981942047E-58, \ 2.04876111892933112E-59, \ 4.7028955186049464E-61, \ 1.00491633674668433E-62, \ 1.9959187047623038E-64, \ 3.6789923736675531E-66, \ 6.2831482675040959E-68, \ 9.925201342288209E-70, \ 1.4475221077412768E-71, \ 1.945364935931307E-73, \ 2.4042822695448614E-75, \ 2.7267496829701407E-77, \ 2.8313374255297656E-79, \ 2.6851895059223692E-81, \ 2.3199549783717045E-83, \ 1.821032672647817E-85, \ 1.29486019972133753E-87, \ 8.3146100960594316E-90, \ 4.8053665090563748E-92, \ 2.49071240066108676E-94, \ 1.15335704284873844E-96, \ 4.75169815023478164E-99, \ 1.733951399870136754E-101, \ 5.57731896834145892E-104, \ 1.573010564351007982E-106, \ 3.867845242632879313E-109, \ 8.239883435606238718E-112, \ 1.5104570697877326124E-114, \ 2.3645657754433596259E-117, \ 3.1349053289923477642E-120, \ 3.48739145376585928069E-123, \ 3.22170074744057989255E-126, \ 2.443048415722317309221E-129, \ 1.5008657805760609578501E-132, \ 7.3592251345721592465131E-136, \ 2.83121162238276011127992E-139, \ 8.3785828758598937096069E-143, \ 1.8637689328976254234922931E-146, \ 3.0323700940390393081087066E-150, \ 3.49260330326226204565809172E-154, \ 2.736761201290944128360070077E-158, \ 1.3888959774881077581342370711E-162, \ 4.28912860126508716947322409477E-167, \ 7.43133882324715291928018394696E-172, \ 6.47421443374096511679045401121E-177, \ 2.42953692988216878005255824922E-182, \ 3.11143287762562176520260181694E-188, \ 9.26127289624597363219192415542E-195, \ 3.07023341560782650495387872798E-202, \ 1.71530871887294016615286222244E-211 ] ) else: print ( '' ) print ( 'LAGUERRE_SET - Fatal error!' ) print ( ' Illegal value of N = %d' % ( n ) ) print ( ' Legal values are 1 to 20, 31/32/33, 63/64/65, 127/128/129' ) exit ( 'LAGUERRE_SET - Fatal error!' ) return x, w def laguerre_set_test ( ): #*****************************************************************************80 # ## LAGUERRE_SET_TEST tests LAGUERRE_SET. # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 15 June 2015 # # Author: # # John Burkardt # import platform print ( '' ) print ( 'LAGUERRE_SET_TEST' ) print ( ' Python version: %s' % ( platform.python_version ( ) ) ) print ( ' LAGUERRE_SET sets a Laguerre rule.' ) print ( '' ) print ( ' I X W' ) for n in range ( 1, 11 ): x, w = laguerre_set ( n ) print ( '' ) for i in range ( 0, n ): print ( ' %8d %24.16g %24.16g' % ( i, x[i], w[i] ) ) # # Terminate. # print ( '' ) print ( 'LAGUERRE_SET_TEST:' ) print ( ' Normal end of execution.' ) return if ( __name__ == '__main__' ): from timestamp import timestamp timestamp ( ) laguerre_set_test ( ) timestamp ( )