## Exponential Integral & Incomplete Gamma function

Hello,

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

I am using the notation from Mathworld here

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

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

 Ok. Solved. I bound the difference by $$\frac{e^m}{2k+1}$$