integrate exp(p(x)) for some polynomial p

From: Cory Hauck (cdhauck_at_math.umd.edu)
Date: 10/25/04 

Date: 25 Oct 2004 07:51:04 -0700

Does anyone know of an efficient quadrature method for integrating

f(x;k)= (x^k)*exp(p(x)), 0 <= k <= n

over the real line? Here n is even and p is any polynomial of degree
n that makes f integrable. In particular p --> -\infty as |x|-->
\infty. The difficulty here is that p could have a zero for
arbitrarily large values of x. In order to maintain accuracy, a
quadrature algorithm has to adjust its domain accordingly to include
such values. Otherwise, some finite amount of mass from f may go
undetected. I can't just expand my domain and calculate by brute
force. That would be wasteful, since a large portion of the mass can
still be supported on a relatively small set.

Any references would be helpful. Thanks.