February 24 2008   3:56:32.971 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 =         8
  ALPHA =     2.00000    
  OUTPUT = "MAT".
%
%  Weights W, abscissas X and range R
%  for a Gauss-Gegenbauer quadrature rule
%  ORDER =        8
%  ALPHA =    2.00000    
%
%  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) =   0.7604803485383879E-02;
  w( 2) =   0.6061158316018705E-01;
  w( 3) =   0.1777998015448417    ;
  w( 4) =   0.2873171451429207    ;
  w( 5) =   0.2873171451429207    ;
  w( 6) =   0.1777998015448415    ;
  w( 7) =   0.6061158316018705E-01;
  w( 8) =   0.7604803485383879E-02;
 
  x( 1) =  -0.8814085756174120    ;
  x( 2) =  -0.6920606182568354    ;
  x( 3) =  -0.4414329761085158    ;
  x( 4) =  -0.1516316642932667    ;
  x( 5) =   0.1516316642932667    ;
  x( 6) =   0.4414329761085158    ;
  x( 7) =   0.6920606182568354    ;
  x( 8) =   0.8814085756174120    ;
 
  r( 1) =  -1.0000000000000000    ;
  r( 2) =   1.0000000000000000    ;
 
GEGENBAUER_RULE:
  Normal end of execution.
 
February 24 2008   3:56:32.976 AM