25 February 2008  12:13:29.237 PM                                               
 
INT_EXACTNESS_GEGENBAUER
  FORTRAN90 version
 
  Investigate the polynomial exactness of a Gauss-Gegenbauer
  quadrature rule by integrating weighted 
  monomials up to a given degree over the [-1,+1] interval.
 
INT_EXACTNESS_GEGENBAUER: User input:
  Quadrature rule X file = "gegen_o16_a0.5_x.txt".
  Quadrature rule W file = "gegen_o16_a0.5_w.txt".
  Quadrature rule R file = "gegen_o16_a0.5_r.txt".
  Maximum degree to check =       35
  Exponent of (1-x^2), ALPHA =   0.500000    
 
  Spatial dimension =        1
  Number of points  =       16
 
  The quadrature rule to be tested is
  a Gauss-Gegenbauer rule
  ORDER =       16
  ALPHA =   0.500000    
 
  Standard rule:
    Integral ( -1 <= x <= +1 ) (1-x^2)^alpha f(x) dx
    is to be approximated by
    sum ( 1 <= I <= ORDER ) w(i) * f(x(i)).
 
  Weights W:
 
  w( 1) =   0.6239551412252181E-02
  w( 2) =   0.2411551965623589E-01
  w( 3) =   0.5121365616644176E-01
  w( 4) =   0.8387420745120895E-01
  w( 5) =   0.1176861850811666    
  w( 6) =   0.1480830941187536    
  w( 7) =   0.1709596635633561    
  w( 8) =   0.1832262859480332    
  w( 9) =   0.1832262859480331    
  w(10) =   0.1709596635633561    
  w(11) =   0.1480830941187535    
  w(12) =   0.1176861850811666    
  w(13) =   0.8387420745120895E-01
  w(14) =   0.5121365616644213E-01
  w(15) =   0.2411551965623589E-01
  w(16) =   0.6239551412252181E-02
 
  Abscissas X:
 
  x( 1) =  -0.9829730996839018    
  x( 2) =  -0.9324722294043558    
  x( 3) =  -0.8502171357296141    
  x( 4) =  -0.7390089172206591    
  x( 5) =  -0.6026346363792564    
  x( 6) =  -0.4457383557765383    
  x( 7) =  -0.2736629900720829    
  x( 8) =  -0.9226835946330200E-01
  x( 9) =   0.9226835946330200E-01
  x(10) =   0.2736629900720829    
  x(11) =   0.4457383557765383    
  x(12) =   0.6026346363792564    
  x(13) =   0.7390089172206591    
  x(14) =   0.8502171357296141    
  x(15) =   0.9324722294043558    
  x(16) =   0.9829730996839018    
 
  Region R:
 
  r( 1) =  -1.0000000000000000    
  r( 2) =   1.0000000000000000    
 
  A Gauss-Gegenbauer rule would be able to exactly
  integrate monomials up to and including degree =       31
 
          Error          Degree  Exponents
 
        0.0000000000000008    0     0
        0.0000000000000002    1     1
        0.0000000000000001    2     2
        0.0000000000000002    3     3
        0.0000000000000006    4     4
        0.0000000000000002    5     5
        0.0000000000000005    6     6
        0.0000000000000001    7     7
        0.0000000000000002    8     8
        0.0000000000000001    9     9
        0.0000000000000024   10    10
        0.0000000000000001   11    11
        0.0000000000000096   12    12
        0.0000000000000000   13    13
        0.0000000000000015   14    14
        0.0000000000000000   15    15
        0.0000000000000049   16    16
        0.0000000000000000   17    17
        0.0000000000000008   18    18
        0.0000000000000000   19    19
        0.0000000000000046   20    20
        0.0000000000000000   21    21
        0.0000000000000069   22    22
        0.0000000000000000   23    23
        0.0000000000000032   24    24
        0.0000000000000000   25    25
        0.0000000000000014   26    26
        0.0000000000000000   27    27
        0.0000000000000044   28    28
        0.0000000000000000   29    29
        0.0000000000000083   30    30
        0.0000000000000000   31    31
        0.0000000282823902   32    32
        0.0000000000000000   33    33
        0.0000002468282487   34    34
        0.0000000000000000   35    35
 
INT_EXACTNESS_GEGENBAUER:
  Normal end of execution.
 
25 February 2008  12:13:29.247 PM