01 March 2008 01:38:33 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 = 1.5

  OUTPUT option is "F90".
!
!  Weights W, abscissas X and range R
!  for a Gauss-Gegenbauer quadrature rule
!  ORDER = 4
!  ALPHA = 1.5
!
!  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(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
  r(2) = 1

GEGENBAUER_RULE:
  Normal end of execution.

01 March 2008 01:38:33 PM