Changes between Version 4 and Version 5 of EllipticTheta1


Ignore:
Timestamp:
03/15/11 13:38:48 (4 years ago)
Author:
rtoy
Comment:

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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