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  <meta http-equiv="Content-Type" content="text/html" charset="us-ascii"/>
  <title>Axiom Documentation</title>
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 <body>
  <div align="center"><img align="middle" src="doctitle.png"/></div>
  <hr/>
  <div align="center">
   <a href="http://dlmf.nist.gov">
    Digital Library of Mathematical Functions
   </a><br/>
   The Gamma Function -- Methods of Computation
  </div>
  <hr/>
<h3>Methods of Computation</h3>

<p>An effective way of computing 
 <m:math display="inline">
  <m:mrow>
   <m:mi mathvariant="normal">&#x0393;</m:mi>
   <m:mrow>
    <m:mo>(</m:mo>
    <m:mi>z</m:mi>
    <m:mo>)</m:mo>
   </m:mrow>
  </m:mrow>
 </m:math> 
in the right half-plane is backward recurrence, beginning with a value 
generated from the 
<a href="dlmfasymptoticexpansions.xhtml#equation3">
 asymptotic expansion
</a>
Or we can use forward recurrence, with an 
<a href="dlmfseriesexpansions.xhtml#equation3">
 initial value
</a>.
For the left half-plane we can continue the backward recurrence or 
make use of the 
<a href="dlmffunctionrelations.xhtml#equation3">
 reflection formula
</a>.
</p>

<p>Similarly for 
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 </m:math>, and the polygamma functions.
</p>

<p>For a comprehensive survey see 
 <a href="http://dlmf.nist.gov/Contents/bib/V#vanderlaan:1984:csf">
  van der Laan and Temme(1984)
 </a>(Chapter III).
 See also 
 <a href="http://dlmf.nist.gov/Contents/bib/B#borwein:1992:feg">
  Borwein and Zucker(1992)
 </a>.
</p>
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