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<H1>gamma function</H1>
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(definition)

<P>
<strong>Definition:</strong>
The gamma function of n, written  <img src="Gamma.gif" tppabs="http://hissa.nist.gov/dads/HTML/Images/Gamma.gif"  border=0 height=10 width=7  alt="Capital Gamma">(n), is   <img src="integ.gif" tppabs="http://hissa.nist.gov/dads/HTML/Images/integ.gif"  border=0 height=20 width=9 alt="integral of" align=middle> <sub>0</sub><sup> <img src="infty.gif" tppabs="http://hissa.nist.gov/dads/HTML/Images/infty.gif"  border=0 height=6  width=13 alt="infinity"></sup> e<sup>-x</sup>x<sup>n-1</sup>dx.  Recursively  <img src="Gamma.gif" tppabs="http://hissa.nist.gov/dads/HTML/Images/Gamma.gif"  border=0 height=10 width=7  alt="Capital Gamma">(n+1) = n <img src="Gamma.gif" tppabs="http://hissa.nist.gov/dads/HTML/Images/Gamma.gif"  border=0 height=10 width=7  alt="Capital Gamma">(n).  For non-negative integers  <img src="Gamma.gif" tppabs="http://hissa.nist.gov/dads/HTML/Images/Gamma.gif"  border=0 height=10 width=7  alt="Capital Gamma">(n+1) = <a href="factorial.html" tppabs="http://hissa.nist.gov/dads/HTML/factorial.html"><em>n!</em></a>.
<P><strong>See also</strong>
<a href="stirlingform.html" tppabs="http://hissa.nist.gov/dads/HTML/stirlingform.html"><em>Stirling's formula</em></a>.
<P><em>Note:
The gamma function is defined for all numbers whereas factorial is (strictly) only defined for non-negative integers.</em>
<P>Author: <a href="terms.html#authorPEB" tppabs="http://hissa.nist.gov/dads/terms.html#authorPEB">PEB</a>

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Entry modified Thu Dec  9 09:16:03 1999.<BR>
HTML page formatted Wed Dec 22 09:35:26 1999.

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