01 March 2008 01:38:23 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

  OUTPUT option is "F77".
c
c  Weights W, abscissas X and range R
c  for a Gauss-Gegenbauer quadrature rule
c  ORDER = 4
c  ALPHA = 1
c
c  Standard rule:
c    Integral ( -1 <= x <= +1 ) (1-x^2)^ALPHA f(x) dx
c    is to be approximated by
c    sum ( 1 <= I <= ORDER ) w(i) * f(x(i)).
c
      w(1) = 0.1569499125956942
      w(2) = 0.5097167540709727
      w(3) = 0.5097167540709727
      w(4) = 0.1569499125956939

      x(1) = -0.7650553239294646
      x(2) = -0.2852315164806451
      x(3) = 0.2852315164806451
      x(4) = 0.7650553239294647

      r(1) = -1
      r(2) = 1

GEGENBAUER_RULE:
  Normal end of execution.

01 March 2008 01:38:23 PM