September  2 2007   9:49:15.844 AM
 
JACOBI_RULE
  FORTRAN90 version
 
  Compute a Gauss-Jacobi rule for approximating
 
    Integral ( -1 <= x <= +1 ) (1-x)^ALPHA (1+x)^BETA f(x) dx
 
  of order ORDER.
 
  The user specifies ORDER, ALPHA, BETA, 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 =     1.00000    
  BETA =     1.00000    
  OUTPUT = "MAT".
%
%  Weights W, abscissas X and range R
%  for a Gauss-Jacobi quadrature rule
%  ORDER =        8
%  ALPHA =    1.00000    
%  BETA  =    1.00000    
%
%  Standard rule:
%    Integral ( -1 <= x <= +1 ) (1-x)^ALPHA (1+x)^BETA f(x) dx
%    is to be approximated by
%    sum ( 1 <= I <= ORDER ) w(i) * f(x(i)).
%
    w( 1) =   0.2059009564912119E-01;
    w( 2) =   0.1021477023603547    ;
    w( 3) =   0.2253365549698504    ;
    w( 4) =   0.3185923136873177    ;
    w( 5) =   0.3185923136873177    ;
    w( 6) =   0.2253365549698507    ;
    w( 7) =   0.1021477023603547    ;
    w( 8) =   0.2059009564912119E-01;
 
    x( 1) =  -0.9195339081664589    ;
    x( 2) =  -0.7387738651055050    ;
    x( 3) =  -0.4779249498104445    ;
    x( 4) =  -0.1652789576663870    ;
    x( 5) =   0.1652789576663870    ;
    x( 6) =   0.4779249498104445    ;
    x( 7) =   0.7387738651055050    ;
    x( 8) =   0.9195339081664589    ;
 
    r(1) =  -1.0000000000000000    ;
    r(2) = 
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;
 
JACOBI_RULE:
  Normal end of execution.
 
September  2 2007   9:49:15.845 AM