01 March 2008 01:38:12 PM

GEGENBAUER_RULE
  C++ version

  Compiled on Mar  1 2008 at 13:37:22.

  Compute a Gauss-Gegenbauer quadrature rule for approximating

    Integral ( -1 <= x <= +1 ) (1-x^2)^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.

  The requested order of the rule is = 4

  The requested value of ALPHA = 0.5

  OUTPUT option is "C++".
//
//  Weights W, abscissas X and range R
//  for a Gauss-Gegenbauer quadrature rule
//  ORDER = 4
//  ALPHA = 0.5
//
//  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)).
//
  w[0] = 0.217078713422706;
  w[1] = 0.5683194499747424;
  w[2] = 0.5683194499747424;
  w[3] = 0.217078713422706;

  x[0] = -0.8090169943749475;
  x[1] = -0.3090169943749475;
  x[2] = 0.3090169943749474;
  x[3] = 0.8090169943749475;

  r[0] = -1;
  r[1] = 1;

GEGENBAUER_RULE:
  Normal end of execution.

01 March 2008 01:38:12 PM