19 January 2008 12:22:09 PM

GEN_HERMITE_RULE
  C++ version

  Compiled on Jan 19 2008 at 12:02:33.

  Compute a generalized Gauss-Hermite rule for approximating

    Integral ( -oo < x < oo ) |X|^ALPHA exp(-x^2) f(x) dx

  of order ORDER and parameter ALPHA.

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

  OPTION is:

    0 to get the standard rule for handling:
      Integral ( -oo < x < oo ) |x|^ALPHA exp(-x^2) f(x) dx

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

    For OPTION = 1, the weights of the standard rule
    are divided by |x|^ALPHA * exp(-x^2).

  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 ALPHA = 1

  The requested value of OPTION = 0

  OUTPUT option is "C++".
//
//  Weights W, abscissas X and range R
//  for a generalized Gauss-Hermite quadrature rule
//  ORDER = 4
//  ALPHA = 1
//
//  OPTION = 0, Standard rule:
//    Integral ( -oo < x < oo ) |x|^ALPHA exp(-x^2) f(x) dx
//    is to be approximated by
//    sum ( 1 <= I <= ORDER ) w(i) * f(x(i)).
//
  w[0] = 0.07322330470336313;
  w[1] = 0.4267766952966369;
  w[2] = 0.4267766952966369;
  w[3] = 0.07322330470336313;

  x[0] = -1.847759065022573;
  x[1] = -0.7653668647301796;
  x[2] = 0.7653668647301796;
  x[3] = 1.847759065022573;

  r[0] = -1e+30;
  r[1] = 1e+30;

GEN_LAGUERRE_RULE:
  Normal end of execution.

19 January 2008 12:22:09 PM