1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Exponential Integral & Incomplete Gamma function

  1. Jan 16, 2008 #1

    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


    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.

    Last edited: Jan 17, 2008
  2. jcsd
  3. Jan 17, 2008 #2
    Maybe I ask should another question first.

    How is the exponential integral function defined for real z less than zero....the integral representation clearly does not converge in that case... is it just analytic continuation or is there an explicit formula...?


  4. Jan 18, 2008 #3
    Ok. Solved. I bound the difference by

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Exponential Integral & Incomplete Gamma function