3 February 2008  11:45:59.415 AM                                               
 
INT_EXACTNESS_GEN_LAGUERRE
  FORTRAN90 version
 
  Investigate the polynomial exactness of a generalized Gauss-Laguerre
  quadrature rule by integrating exponentially weighted 
  monomials up to a given degree over the [0,+oo) interval.
 
  The rule may be defined on another interval, [A,+oo)
  in which case it is adjusted to the [0,+oo) interval.
 
INT_EXACTNESS_GEN_LAGUERRE: User input:
  Quadrature rule X file = "gen_lag_o16_a0.5_modified_x.txt".
  Quadrature rule W file = "gen_lag_o16_a0.5_modified_w.txt".
  Quadrature rule R file = "gen_lag_o16_a0.5_modified_r.txt".
  Maximum degree to check =       35
  Weighting function exponent ALPHA =   0.500000    
 
  Spatial dimension =        1
  Number of points  =       16
 
  The quadrature rule to be tested is
  a generalized Gauss-Laguerre rule
  ORDER =       16
  A =        0.00000    
  ALPHA =   0.500000    
 
  OPTION = 1, modified rule:
    Integral ( A <= x < oo ) f(x) dx
    is to be approximated by
    sum ( 1 <= I <= ORDER ) w(i) * f(x(i)).
 
  Weights W:
 
  w( 1) =   0.2950148257926292    
  w( 2) =   0.5926504061509453    
  w( 3) =   0.8956575998744516    
  w( 4) =    1.207063433953284    
  w( 5) =    1.530352787791976    
  w( 6) =    1.869714179339352    
  w( 7) =    2.230395748423061    
  w( 8) =    2.619252244761896    
  w( 9) =    3.045634801992271    
  w(10) =    3.522929682017350    
  w(11) =    4.071417057880741    
  w(12) =    4.724080738693911    
  w(13) =    5.539909876059123    
  w(14) =    6.639993574123777    
  w(15) =    8.335658835078922    
  w(16) =    11.89633502881635    
 
  Abscissas X:
 
  x( 1) =   0.1473991846163110    
  x( 2) =   0.5909018112431889    
  x( 3) =    1.334487511614577    
  x( 4) =    2.385011552004654    
  x( 5) =    3.752567873874769    
  x( 6) =    5.451062939568397    
  x( 7) =    7.499085532907372    
  x( 8) =    9.921219136072430    
  x( 9) =    12.75005546011707    
  x(10) =    16.02938636037513    
  x(11) =    19.81951287710202    
  x(12) =    24.20668064346831    
  x(13) =    29.32145610335233    
  x(14) =    35.37955078717556    
  x(15) =    42.79325597075464    
  x(16) =    52.61836625575324    
 
  Region R:
 
  r( 1) =    0.000000000000000    
  r( 2) =   0.1000000000000000E+31
 
  A generalized Gauss-Laguerre rule would be able to exactly
  integrate monomials up to and including degree =       31
 
          Error          Degree
 
        0.0000000000000005    0
        0.0000000000000012    1
        0.0000000000000013    2
        0.0000000000000006    3
        0.0000000000000004    4
        0.0000000000000002    5
        0.0000000000000001    6
        0.0000000000000000    7
        0.0000000000000001    8
        0.0000000000000002    9
        0.0000000000000002   10
        0.0000000000000024   11
        0.0000000000000008   12
        0.0000000000000046   13
        0.0000000000000044   14
        0.0000000000000034   15
        0.0000000000000015   16
        0.0000000000000028   17
        0.0000000000000035   18
        0.0000000000000009   19
        0.0000000000000054   20
        0.0000000000000032   21
        0.0000000000000008   22
        0.0000000000000088   23
        0.0000000000000031   24
        0.0000000000000048   25
        0.0000000000000028   26
        0.0000000000000015   27
        0.0000000000000029   28
        0.0000000000000078   29
        0.0000000000000055   30
        0.0000000000000028   31
        0.0000000011898407   32
        0.0000000199430886   33
        0.0000001720073247   34
        0.0000010170435781   35
 
INT_EXACTNESS_GEN_LAGUERRE:
  Normal end of execution.
 
 3 February 2008  11:45:59.419 AM