01 March 2008 01:38:46 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 = 8

  The requested value of ALPHA = 2

  OUTPUT option is "MAT".
%
%  Weights W, abscissas X and range R
%  for a Gauss-Gegenbauer quadrature rule
%  ORDER = 8
%  ALPHA = 2
%
%  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) = 0.007604803485383879;
  w(2) = 0.06061158316018705;
  w(3) = 0.1777998015448417;
  w(4) = 0.2873171451429207;
  w(5) = 0.2873171451429207;
  w(6) = 0.1777998015448415;
  w(7) = 0.06061158316018705;
  w(8) = 0.007604803485383879;

  x(1) = -0.881408575617412;
  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) = 0.881408575617412;

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

GEGENBAUER_RULE:
  Normal end of execution.

01 March 2008 01:38:46 PM