Group Abstract Group Abstract

Message Boards Message Boards

0
|
4K Views
|
5 Replies
|
0 Total Likes
View groups...
Share
Share this post:

Incomplete answer of Series involves generalized incomplete gamma function

Why Mathematica couldn't perform the series: 

Normal[FullSimplify[Series[-(-1)^(n + k)*Sin[Pi*\[Lambda]]/Pi
    *Gamma[\[Lambda], 0, 1], {\[Lambda], 0, 1}]]]

and just give the incomplete answer

(-1)^(k + n) \[Lambda] Gamma[0, 1] + (-1)^(
  1 + k + n) \[Lambda] Gamma[\[Lambda], 0]

The difficulty is the indeterminate problem. How to circumvent the issue? Thanks.
POSTED BY: MEK MUS
5 Replies
Sort By:
POSTED BY: MEK MUS

This is not going to improve on the result, because the assumption of z>0 does not say anything about -n-k-z. So version 13.0.1 will not give a result that avoids using Gamma[-k - n - z, 0].

To repeat, Gamma[whatever,0] is at a branch point in the second argument. So the first needs to be sufficiently restricted if you want to get a true series result.

POSTED BY: Daniel Lichtblau
POSTED BY: Daniel Lichtblau
POSTED BY: MEK MUS

It looks like we are getting two different results. Mine was from using version 13.0.1. What version are you using?
POSTED BY: Daniel Lichtblau
Reply to this discussion
Community posts can be styled and formatted using the Markdown syntax.
Tag limit exceeded
Note: Only the first five people you tag will receive an email notification; the other tagged names will appear as links to their profiles.
Reply Preview
Attachments
Remove
or Discard