jtheta3

ljtheta3

Evaluates the third Jacobi theta function.

Evaluation of the Jacobi theta functions and related
functions: Weierstrass elliptic function, Weierstrass sigma function,
Weierstrass zeta function, Klein j-function, Dedekind eta function,
lambda modular function, Jacobi elliptic functions, Neville theta
functions, Eisenstein series, lemniscate elliptic functions, elliptic
alpha function, Rogers-Ramanujan continued fractions, and Dixon
elliptic functions. Complex values of the variable are supported.

Stc3<a9>phane Laurent

jacobi

Jacobi Theta Functions and Related Functions

Stéphane Laurent

Mikael Fremling

jtheta3 function

<dl><dt>z</dt>
<dd>complex number, vector, or matrix</dd>
<dt>tau</dt>
<dd>lattice parameter, a complex number with strictly positive 
imaginary part; the two complex numbers <code>tau</code> and <code>q</code> are 
related by <code>q = exp(1i*pi*tau)</code>, and only one of them must be 
supplied</dd>
<dt>q</dt>
<dd>the nome, a complex number whose modulus is strictly less than one, 
but not zero</dd></dl>

Arguments

Jacobi theta function three — jtheta3

<dl>

<dt>z</dt>
<dd>complex number, vector, or matrix</dd>


<dt>tau</dt>
<dd>lattice parameter, a complex number with strictly positive 
imaginary part; the two complex numbers <code>tau</code> and <code>q</code> are 
related by <code>q = exp(1i*pi*tau)</code>, and only one of them must be 
supplied</dd>


<dt>q</dt>
<dd>the nome, a complex number whose modulus is strictly less than one, 
but not zero</dd>

</dl>

jtheta3: Jacobi theta function three

Description

Usage

Value

Arguments

Examples