File r37/lisp/csl/html/r37_0487.html artifact 18e9aeb589 part of check-in 1b32ca91d4

<A NAME=EllipticTHETA>

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



<B>ELLIPTICTHETA</B> _ _ _  _ _ _  _ _ _  _ _ _ <B>operator</B><P>
<P>
 
The <em>EllipticTheta</em> operator returns one of the four Theta 
functions. It cannot except any number other than 1,2,3 or 4 as 
its first argument. 
<P>
<P>
 <P> <H3> 
syntax: </H3>
<em>EllipticTheta</em>(&lt;integer&gt;,&lt;expression&gt;,&lt;integer&gt;) 
<P>
<P>
<P>
 <P> <H3> 
examples: </H3>
<P><PRE><TT>
EllipticTheta(1, 1.4, 0.72) 

  0.91634775373  


EllipticTheta(2, 3.9, 6.1 ) 

  -48.0202736969 + 20.9881034377 i 


EllipticTheta(3, 0.67, 0.2) 

  1.0083077448   


EllipticTheta(4, 8, 0.75) 

  0.894963369304 


EllipticTheta(5, 1, 0.1) 

  ***** In EllipticTheta(a,u,m); a = 1,2,3 or 4.   

</TT></PRE><P>Theta functions are important because every one of the Jacobian 
Elliptic functions can be expressed as the ratio of two theta functions. 
<P>
<P>
<P>