A Question About the Gamma Function

For the discussion of math. Duh.

Moderators: gmalivuk, Moderators General, Prelates

philt
Posts: 1
Joined: Wed Oct 27, 2010 11:46 am UTC

A Question About the Gamma Function

Postby philt » Wed Oct 27, 2010 12:32 pm UTC

I've got a problem for a class that requires me to modify the gamma function from its usual form:
[math]\Gamma(s) = \int_0^\infty x^{s-1} e^{-x}\,{\rm d}x\,[/math]
to the form
[math]\Gamma(s) = f(s)\int_0^\infty e^{-A(y)/ \xi(s)}\,{\rm d}y\,[/math]
through 'a suitable change of the integration variable'. It's not too hard to get the right form of the exponential (eg [imath]y = e^{-x}[/imath]), but I never manage to keep the limits the same. I can't find anything online or in my textbooks, and would really appreciate any help at all.

EDIT: done it! And only a few hours before the deadline :) If anyone's interested the substitution is (annoyingly simple) [imath]x = (s-1)y[/imath]. If anyone wants to see where this comes from (it's not just random guessing!), let me know and I'll type it up.

Return to “Mathematics”

Who is online

Users browsing this forum: No registered users and 15 guests