Hello, everyone. After my discovery some time ago of the gamma function \int_a^b x^{-n}e^{-x}dx(adsbygoogle = window.adsbygoogle || []).push({});

(where b = infinity and a = 0....sorry, haven't quite figured out LaTex yet....and actually the foregoing is the factorial function [I think it's silly that the argument has to be shifted down by one]), I've tried my darnedest to evaluate this integral for non-integer values.

I've figured out how to do it for n = 1/2 by using the u-substitution x = u^2 and then converting to polar coordinates to yield \int_a^b x^{-n}e^{-x}dx = (pi^.5)/2. But I'm stuck as far as using any other rational numbers, much less irrational numbers for n.

When I try to evaluate the function for non-integers, the only sensible thing to do, it seems, is to integrate by parts. But then I get an infinite number of parts (all of which create a pattern, but I don't know how to make numberical sense out of this pattern).

Could someone help me out here?

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# How to evaluate the gamma function for non-integers

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