Re: Factorials on the 86
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Re: Factorials on the 86
In article <6c37vg$geq$1@hecate.umd.edu>, marshall@astro.umd.edu (James
Marshall) wrote:
>In article <34E4BC0D.23EA71D6@aol.com> Todd Stanley <toddestan@aol.com>
writes:
>>What is the Gamma function and what does it do (as in what does the
>>number it give out mean)?
>
>Well, it's kind of like a factorial function for non-integers. :) The
>definition I found in Schaum's Mathematical Handbook is:
>
>Gamma(n) = Integral( t^(n-1)*exp(-t), t, 0, infinity ) for n>0
>
>The book also has a graph of the Gamma function which includes negative
>numbers, but I don't see a definition for how to get them with a quick
>look at it.
The fundamental identity for the Gamma function is Gamma(x + 1) = x*Gamma(x).
This implies that Gamma(x) = Gamma(x + 1)/x.
Using this version of the identity, you can get Gamma(x) for -1 < x < 0
from the values of Gamma(x) for 0 < x < 1 (use the integral). Repeat this
process as needed to deal with any non-integer negative x.
Gene
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