Changes between Version 4 and Version 5 of EllipticTheta1

Timestamp:

03/15/11 06:38:48 (2 years ago)

Author:

rtoy

Comment:

--

EllipticTheta1

@@ -1 +1 @@
 = Elliptic Theta Functions =
 
-All of the elliptic theta functions are functions of two parameters.
-The second parameter ''q'' is the ''nome'' and must satisfy 
-{{{|q| < 1}}}.
+== Introduction ==
 
-== Theta 1 ==
+All of the elliptic theta functions are functions of two parameters:
+the argument ''z'' and a second argument.  For these routines the
+second argument is the nome ''q'', {{{|q| < 1}}} .  Some references
+use the the lattice parameter ''tau'', with the imaginary part of
+''tau'' strictly positive.
+
+The nome and lattice parameter are related by {{{q = exp(%i*%pi*tau)}}}.
+
+=== Theta 1 ===
 {{{(elliptic-theta-1 z q)}}}
 
@@ -13 +19 @@
 }}}
 
-== Theta 2 ==
+=== Theta 2 ===
 {{{(elliptic-theta-2 z q)}}}
 
@@ -21 +27 @@
 }}}
 
-== Theta 3 ==
+=== Theta 3 ===
 {{{(elliptic-theta-3 z q)}}}
 
@@ -29 +35 @@
 }}}
 
-== Theta 4 ==
+=== Theta 4 ===
 {{{(elliptic-theta-4 z q)}}}