Changes between Version 4 and Version 5 of EllipticTheta1

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Timestamp:
03/15/11 06:38:48 (3 years ago)
Author:
rtoy
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  • EllipticTheta1

    v4 v5  
    11= Elliptic Theta Functions = 
    22 
    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 == 
    64 
    7 == Theta 1 == 
     5All of the elliptic theta functions are functions of two parameters: 
     6the argument ''z'' and a second argument.  For these routines the 
     7second argument is the nome ''q'', {{{|q| < 1}}} .  Some references 
     8use the the lattice parameter ''tau'', with the imaginary part of 
     9''tau'' strictly positive. 
     10 
     11The nome and lattice parameter are related by {{{q = exp(%i*%pi*tau)}}}. 
     12 
     13=== Theta 1 === 
    814{{{(elliptic-theta-1 z q)}}} 
    915 
     
    1319}}} 
    1420 
    15 == Theta 2 == 
     21=== Theta 2 === 
    1622{{{(elliptic-theta-2 z q)}}} 
    1723 
     
    2127}}} 
    2228 
    23 == Theta 3 == 
     29=== Theta 3 === 
    2430{{{(elliptic-theta-3 z q)}}} 
    2531 
     
    2935}}} 
    3036 
    31 == Theta 4 == 
     37=== Theta 4 === 
    3238{{{(elliptic-theta-4 z q)}}} 
    3339