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I need to compare an exponential integral [tex]-E_{-2k}(-m)[/tex] -where k is a positive integer and m just a real number- to a Gamma function [tex]\frac{1}{m^{2k+1}}\Gamma(2k+1)[/tex].

I am using the notation from Mathworld here

http://mathworld.wolfram.com/ExponentialIntegral.html

http://mathworld.wolfram.com/IncompleteGammaFunction.html

I am interested in the behaviour of their difference as [tex]k\to\infty[/tex]. It seems to tend to zero, but are there any estimates as to how fast the difference goes to zero?

Thansk for any comments.

-Pere

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# Exponential Integral & Incomplete Gamma function

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