25 February 2008   4:56:14.023 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_o8_a0.5_x.txt".
  Quadrature rule W file = "gegen_o8_a0.5_w.txt".
  Quadrature rule R file = "gegen_o8_a0.5_r.txt".
  Maximum degree to check =       19
  Exponent of (1-x^2), ALPHA =   0.500000    
 
  Spatial dimension =        1
  Number of points  =        8
 
  The quadrature rule to be tested is
  a Gauss-Gegenbauer rule
  ORDER =        8
  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) =   0.4083294770910693E-01
  w( 2) =   0.1442256007956728    
  w( 3) =   0.2617993877991495    
  w( 4) =   0.3385402270935191    
  w( 5) =   0.3385402270935191    
  w( 6) =   0.2617993877991495    
  w( 7) =   0.1442256007956728    
  w( 8) =   0.4083294770910754E-01
 
  Abscissas X:
 
  x( 1) =  -0.9396926207859084    
  x( 2) =  -0.7660444431189780    
  x( 3) =  -0.5000000000000000    
  x( 4) =  -0.1736481776669303    
  x( 5) =   0.1736481776669303    
  x( 6) =   0.5000000000000000    
  x( 7) =   0.7660444431189780    
  x( 8) =   0.9396926207859084    
 
  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 =       15
 
          Error          Degree  Exponents
 
        0.0000000000000003    0     0
        0.0000000000000006    1     1
        0.0000000000000008    2     2
        0.0000000000000005    3     3
        0.0000000000000010    4     4
        0.0000000000000004    5     5
        0.0000000000000016    6     6
        0.0000000000000004    7     7
        0.0000000000000021    8     8
        0.0000000000000003    9     9
        0.0000000000000052   10    10
        0.0000000000000003   11    11
        0.0000000000000126   12    12
        0.0000000000000003   13    13
        0.0000000000000022   14    14
        0.0000000000000002   15    15
        0.0006993006993020   16    16
        0.0000000000000002   17    17
        0.0032908268202344   18    18
        0.0000000000000002   19    19
 
INT_EXACTNESS_GEGENBAUER:
  Normal end of execution.
 
25 February 2008   4:56:14.102 PM