19 January 2008 12:22:56 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 = 0

  The requested value of OPTION = 1

  OUTPUT option is "F90".
!
!  Weights W, abscissas X and range R
!  for a generalized Gauss-Hermite quadrature rule
!  ORDER = 4
!  ALPHA = 0
!
!  OPTION = 1, modified rule:
!    Integral ( -oo < x < oo ) f(x) dx
!    is to be approximated by
!    sum ( 1 <= I <= ORDER ) w(i) * f(x(i)).
!
  w(1) = 1.240225817695815
  w(2) = 1.05996448289497
  w(3) = 1.05996448289497
  w(4) = 1.240225817695815

  x(1) = -1.650680123885784
  x(2) = -0.5246476232752902
  x(3) = 0.5246476232752902
  x(4) = 1.650680123885784

  r(1) = -1e+30
  r(2) = 1e+30

GEN_LAGUERRE_RULE:
  Normal end of execution.

19 January 2008 12:22:56 PM