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<A NAME=LegendreP>

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



<B>LEGENDREP</B> _ _ _  _ _ _  _ _ _  _ _ _ <B>operator</B><P>
<P>
 
The binary <em>LegendreP</em> operator computes the nth Legendre 
Polynomial which is 
a special case of the nth Jacobi Polynomial with 
<P>
<P>
LegendreP(n,x) := JacobiP(n,0,0,x) 
<P>
<P>
The ternary form returns the associated Legendre Polynomial (see below). 
<P>
<P>
 <P> <H3> 
syntax: </H3>
<em>LegendreP</em>(&lt;integer&gt;,&lt;expression&gt;) or 
<P>
<P>
<em>LegendreP</em>(&lt;integer&gt;,&lt;expression&gt;,&lt;expression&gt;) 
<P>
<P>
<P>
 <P> <H3> 
examples: </H3>
<P><PRE><TT>
LegendreP(3,xx); 

          2
  xx*(5*xx   - 3)
  ----------------
         2



LegendreP(3,2,xx); 

              2
  15*xx*( - xx   + 1)

</TT></PRE><P>The ternary form of the operator <em>LegendreP</em> is the associa
ted 
Legendre Polynomial defined as 
 <P>
<P>
P(n,m,x) = (-1)**m * (1-x**2)**(m/2) * df(LegendreP(n,x),x,m) 
<P>
<P>
<P>