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 Timestamp:

03/15/11 13:38:48 (6 years ago)
 Author:

rtoy
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v4

v5


1  1  = Elliptic Theta Functions = 
2  2  
3   All of the elliptic theta functions are functions of two parameters. 
4   The second parameter ''q'' is the ''nome'' and must satisfy 
5   {{{q < 1}}}. 
 3  == Introduction == 
6  4  
7   == Theta 1 == 
 5  All of the elliptic theta functions are functions of two parameters: 
 6  the argument ''z'' and a second argument. For these routines the 
 7  second argument is the nome ''q'', {{{q < 1}}} . Some references 
 8  use the the lattice parameter ''tau'', with the imaginary part of 
 9  ''tau'' strictly positive. 
 10  
 11  The nome and lattice parameter are related by {{{q = exp(%i*%pi*tau)}}}. 
 12  
 13  === Theta 1 === 
8  14  {{{(elliptictheta1 z q)}}} 
9  15  
… 
… 

13  19  }}} 
14  20  
15   == Theta 2 == 
 21  === Theta 2 === 
16  22  {{{(elliptictheta2 z q)}}} 
17  23  
… 
… 

21  27  }}} 
22  28  
23   == Theta 3 == 
 29  === Theta 3 === 
24  30  {{{(elliptictheta3 z q)}}} 
25  31  
… 
… 

29  35  }}} 
30  36  
31   == Theta 4 == 
 37  === Theta 4 === 
32  38  {{{(elliptictheta4 z q)}}} 
33  39  