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Numerical integration over half-infinite intervals

• To: mathgroup at smc.vnet.net
• Subject: [mg60273] Numerical integration over half-infinite intervals
• From: "Alan" <info at optioncity.REMOVETHIS.net>
• Date: Fri, 9 Sep 2005 04:07:17 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

I do a lot of 1D NIntegrates over half-infinite domains [0,Infinity).
Sometimes you can simply put Infinity as an upper
bound and Mathematica will return an answer. In that
case, I don't have a problem.

But, sometimes, this fails or takes too
long, and I am forced to truncate the integral.

Let's assume my integral converges, is not zero, and my
integrand is relatively smooth with a few derivatives, at least.
Suppose each finite truncated integral can be successfully computed to
the same fixed PrecisionGoal.

Given that, my questions:

Is it possible to extrapolate these truncated results to a
limit with a known precision? If so, how, and how does that
precision relate to the fixed PrecisionGoal above?

Thanks,
alan