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asymptotic expansion

• To: mathgroup at smc.vnet.net
• Subject: [mg104196] asymptotic expansion
• From: Mauro <msmscarlatti at googlemail.com>
• Date: Thu, 22 Oct 2009 22:34:24 -0400 (EDT)

I have to calculate an integral from x0 > 0 to infinity of a function
like

ln (F(x)) / x

where F(x) is a function which tends to 1 for x going to infinity.
Since the integrand goes to zero very slowly, I am trying to calculate
the asymptotic expansion of the integral by taking the power series of
the integrand and integrating term by term. Unfortunately F(x) is a
very messy function, so it's difficult to do the calculations by hand.
What is the best way of using Mathematica for this type of
calculation?

Thanks.