- #1
Pere Callahan
- 586
- 1
Hello,
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.htmlI 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
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.htmlI 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
Last edited: