jellip

Evaluation of the Jacobi elliptic functions.

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

jellip function

<dl><dt>kind</dt>
<dd>a string with two characters among <code>"s"</code>, <code>"c"</code>, 
<code>"d"</code> and <code>"n"</code>; this string specifies the function: the two 
letters respectively denote the basic functions \(sn\), \(cn\), 
\(dn\) and \(1\), and the string specifies the ratio of two such 
functions, e.g. \(ns = 1/sn\) and \(cd = cn/dn\)</dd>
<dt>u</dt>
<dd>a complex number, vector or matrix</dd>
<dt>tau</dt>
<dd>complex number with strictly positive imaginary part; it is 
related to <code>m</code> and only one of them must be supplied</dd>
<dt>m</dt>
<dd>the "parameter", square of the elliptic modulus; it is related to 
<code>tau</code> and only one of them must be supplied</dd></dl>

Arguments

Jacobi elliptic functions — jellip

<dl>

<dt>kind</dt>
<dd>a string with two characters among <code>"s"</code>, <code>"c"</code>, 
<code>"d"</code> and <code>"n"</code>; this string specifies the function: the two 
letters respectively denote the basic functions \(sn\), \(cn\), 
\(dn\) and \(1\), and the string specifies the ratio of two such 
functions, e.g. \(ns = 1/sn\) and \(cd = cn/dn\)</dd>


<dt>u</dt>
<dd>a complex number, vector or matrix</dd>


<dt>tau</dt>
<dd>complex number with strictly positive imaginary part; it is 
related to <code>m</code> and only one of them must be supplied</dd>


<dt>m</dt>
<dd>the "parameter", square of the elliptic modulus; it is related to 
<code>tau</code> and only one of them must be supplied</dd>

</dl>

jellip: Jacobi elliptic functions

Description

Usage

Value

Arguments

Examples