File r37/lisp/csl/html/r37_0500.html artifact 4023631e61 part of check-in a57e59ec0d

<A NAME=ChebyshevU>

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



<B>CHEBYSHEVU</B> _ _ _  _ _ _  _ _ _  _ _ _ <B>operator</B><P>
<P>
 
The <em>ChebyshevU</em> operator returns the nth Chebyshev U Polynomial (of the 

second kind). 
<P>
<P>
 <P> <H3> 
syntax: </H3>
<em>ChebyshevU</em>(&lt;integer&gt;,&lt;expression&gt;) 
<P>
<P>
<P>
 <P> <H3> 
examples: </H3>
<P><PRE><TT>
ChebyshevU(3,xx); 

          2
  4*x*(2*x   - 1) 



ChebyshevU(3,4); 

  496

</TT></PRE><P>Chebyshev's U polynomials are computed using the recurrence relati
on: 
<P>
<P>
ChebyshevU(n,x) := 2x*ChebyshevU(n-1,x) - ChebyshevU(n-2,x) with 
<P>
<P>
ChebyshevU(0,x) := 0 and ChebyshevU(1,x) := 2x 
<P>
<P>
<P>
<P>