Jacques Duilio Brancher wrote:
> I'm looking for a Fortran90 code to evaluate some improper integrals.
> The limits of integration are zero and infinity. For that, I need
> the weights and roots of the Laguerre Polinomial.
"A Fortran subroutine for numerical integration in h^P" by Sikorski, Stenger
and Schwing appeared in ACM Transactions on Mathematical Software 10 (1984)
as algorithm 614.
It can handle either finite or infinite intervals.
An alternative is to apply a transformation that converts the infinite interval
to a finite interval. Such transformations usually introduce a singularity
into the integrand at the origin, that should be removed or weakened by yet
another transformation.
Another alternative is to discover the abscissa at which the integrand
underflows, in the arithmetic you propose to use, and integrate only to that
abscissa using a procedure designed for finite intervals. If the integrand
oscillates, look for where the envelope of it underflows.
Best regards,
Van Snyder
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