February 24 2008   3:56:25.097 AM
 
GEGENBAUER_RULE
  FORTRAN90 version
 
  Compute a Gauss-Gegenbauer rule for approximating
 
    Integral ( -1 <= x <= +1 ) (1-x)^ALPHA (1+x)^ALPHA f(x) dx
 
  of order ORDER.
 
  The user specifies ORDER, ALPHA, and OUTPUT.
 
  OUTPUT is:
 
  "C++" for printed C++ output;
  "F77" for printed Fortran77 output;
  "F90" for printed Fortran90 output;
  "MAT" for printed MATLAB output;
 
  or:
 
  "filename" to generate 3 files:
 
    filename_w.txt - the weight file
    filename_x.txt - the abscissa file.
    filename_r.txt - the region file.
 
  Input summary:
 
  ORDER =         4
  ALPHA =     1.50000    
  OUTPUT = "F90".
!
!  Weights W, abscissas X and range R
!  for a Gauss-Gegenbauer quadrature rule
!  ORDER =        4
!  ALPHA =    1.50000    
!
!  Standard rule:
!    Integral ( -1 <= x <= +1 ) (1-x)^ALPHA (1+x)^ALPHA f(x) dx
!    is to be approximated by
!    sum ( 1 <= I <= ORDER ) w(i) * f(x(i)).
!
  w( 1) =   0.1231363810622288    
  w( 2) =   0.4659122414858576    
  w( 3) =   0.4659122414858576    
  w( 4) =   0.1231363810622288    
 
  x( 1) =  -0.7274123897403673    
  x( 2) =  -0.2662164819319194    
  x( 3) =   0.2662164819319194    
  x( 4) =   0.7274123897403673    
 
  r( 1) =  -1.0000000000000000    
  r( 2) =   1.0000000000000000    
 
GEGENBAUER_RULE:
  Normal end of execution.
 
February 24 2008   3:56:25.101 AM