File r37/lisp/csl/html/r37_0521.html artifact 31f9918432 part of check-in 52fc28dabe

<A NAME=STIRLING1>

<TITLE>STIRLING1</TITLE></A>
<b><a href=r37_idx.html>INDEX</a></b><p><p>



<B>STIRLING1</B> _ _ _  _ _ _  _ _ _  _ _ _ <B>operator</B><P>
<P>
 
The <em>Stirling1</em> operator returns the Stirling Numbers S(n,m) of the first
 
kind, i.e. the number of permutations of n symbols which have exactly m cycles 
(divided by (-1)**(n-m)). 
<P>
<P>
 <P> <H3> 
syntax: </H3>
<em>Stirling1</em>(&lt;integer&gt;,&lt;integer&gt;) 
<P>
<P>
<P>
 <P> <H3> 
examples: </H3>
<P><PRE><TT>
Stirling1 (17,4); 

  -87077748875904 


Stirling1 (n,n-1); 

  -gamma(n+1)
  -------------
  2*gamma(n-1)

</TT></PRE><P>The operator <em>Stirling1</em> evaluates the Stirling numbers of 
the 
first kind by rulesets for special cases or by a computing the closed 
form, which is a series involving the operators 
<A HREF=r37_0520.html>BINOMIAL</A> 
and 
<A HREF=r37_0522.html>STIRLING2</A>. 
<P>
<P>
<P>