18 January 2008 09:39:03 AM

GEN_LAGUERRE_RULE
  C++ version

  Compiled on Jan 18 2008 at 09:36:44.

  Compute a generalized Gauss-Laguerre rule for approximating

    Integral ( A <= x < oo ) x^ALPHA exp(-x) f(x) dx

  of order ORDER and parameter ALPHA.

  For now, A is fixed at 0.0.

  The user specifies ORDER, ALPHA, OPTION, and OUTPUT.

  OPTION is:

    0 to get the standard rule for handling:
      Integral ( A <= x < oo ) x^ALPHA exp(-x) f(x) dx

    1 to get the modified rule for handling:
      Integral ( A <= x < oo )                 f(x) dx

    For OPTION = 1, the weights of the standard rule
    are multiplied by x^(-ALPHA) * exp(+x).

  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 ALPHA = 1.5

  The requested value of OPTION = 0

  OUTPUT option is "MAT".
%
%  Weights W, abscissas X and range R
%  for a generalized Gauss-Laguerre quadrature rule
%  ORDER = 8
%  A = 0
%  ALPHA = 1.5
%
%  OPTION = 0, Standard rule:
%   Integral ( A <= x < oo ) x^ALPHA exp(-x) f(x) dx
%    is to be approximated by
%    sum ( 1 <= I <= ORDER ) w(i) * f(x(i)).
%
  w(1) = 0.1900505753913609;
  w(2) = 0.5604380973781606;
  w(3) = 0.4360070168210791;
  w(4) = 0.1274485793102171;
  w(5) = 0.01476947042302809;
  w(6) = 0.0006195794633122049;
  w(7) = 7.16438948756851e-06;
  w(8) = 1.070030801415182e-08;

  x(1) = 0.5487420203051167;
  x(2) = 1.638181097086517;
  x(3) = 3.315036043679075;
  x(4) = 5.640313098679649;
  x(5) = 8.715661629230398;
  x(6) = 12.71773901227562;
  x(7) = 17.99242472404181;
  x(8) = 25.43190237470182;

  r(1) = 0;
  r(2) = 1e+30;

GEN_LAGUERRE_RULE:
  Normal end of execution.

18 January 2008 09:39:03 AM