3 February 2008  11:45:59.274 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_x.txt".
  Quadrature rule W file = "gen_lag_o16_a0.5_w.txt".
  Quadrature rule R file = "gen_lag_o16_a0.5_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 = 0, standard rule:
    Integral ( A <= x < oo ) x^alpha exp(-x) f(x) dx
    is to be approximated by
    sum ( 1 <= I <= ORDER ) w(i) * f(x(i)).
 
  Weights W:
 
  w( 1) =   0.9774098913713274E-01
  w( 2) =   0.2523079012122731    
  w( 3) =   0.2724198251520776    
  w( 4) =   0.1716635071262904    
  w( 5) =   0.6954026102655395E-01
  w( 6) =   0.1873480877845603E-01
  w( 7) =   0.3381229238954949E-02
  w( 8) =   0.4052556900801655E-03
  w( 9) =   0.3156131814886896E-04
  w(10) =   0.1541304259364148E-05
  w(11) =   0.4474937802762097E-07
  w(12) =   0.7136037163751600E-09
  w(13) =   0.5532849784136906E-11
  w(14) =   0.1703727514691121E-13
  w(15) =   0.1418249588844851E-16
  w(16) =   0.1213712303922958E-20
 
  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
 
        0.0000000000000006    0
        0.0000000000000012    1
        0.0000000000000013    2
        0.0000000000000008    3
        0.0000000000000004    4
        0.0000000000000002    5
        0.0000000000000001    6
        0.0000000000000005    7
        0.0000000000000007    8
        0.0000000000000008    9
        0.0000000000000016   10
        0.0000000000000004   11
        0.0000000000000028   12
        0.0000000000000025   13
        0.0000000000000060   14
        0.0000000000000049   15
        0.0000000000000000   16
        0.0000000000000038   17
        0.0000000000000040   18
        0.0000000000000014   19
        0.0000000000000052   20
        0.0000000000000032   21
        0.0000000000000006   22
        0.0000000000000089   23
        0.0000000000000031   24
        0.0000000000000046   25
        0.0000000000000030   26
        0.0000000000000011   27
        0.0000000000000034   28
        0.0000000000000086   29
        0.0000000000000045   30
        0.0000000000000022   31
        0.0000000011898415   32
        0.0000000199430896   33
        0.0000001720073255   34
        0.0000010170435789   35
 
INT_EXACTNESS_GEN_LAGUERRE:
  Normal end of execution.
 
 3 February 2008  11:45:59.279 AM