Evaluation of the Weierstrass elliptic function and its 
 derivatives.

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

wp function

<dl><dt>z</dt>
<dd>complex number, vector or matrix</dd>
<dt>g</dt>
<dd>the elliptic invariants, a vector of two complex numbers; only 
one of <code>g</code>, <code>omega</code> and <code>tau</code> must be given</dd>
<dt>omega</dt>
<dd>the half-periods, a vector of two complex numbers; only 
one of <code>g</code>, <code>omega</code> and <code>tau</code> must be given</dd>
<dt>tau</dt>
<dd>the half-periods ratio; supplying <code>tau</code> is equivalent to 
supply <code>omega = c(1/2, tau/2)</code></dd>
<dt>derivative</dt>
<dd>differentiation order, an integer between 0 and 3</dd></dl>

Arguments

Weierstrass elliptic function — wp

<dl>

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


<dt>g</dt>
<dd>the elliptic invariants, a vector of two complex numbers; only 
one of <code>g</code>, <code>omega</code> and <code>tau</code> must be given</dd>


<dt>omega</dt>
<dd>the half-periods, a vector of two complex numbers; only 
one of <code>g</code>, <code>omega</code> and <code>tau</code> must be given</dd>


<dt>tau</dt>
<dd>the half-periods ratio; supplying <code>tau</code> is equivalent to 
supply <code>omega = c(1/2, tau/2)</code></dd>


<dt>derivative</dt>
<dd>differentiation order, an integer between 0 and 3</dd>

</dl>

wp: Weierstrass elliptic function

Description

Usage

Value

Arguments

Examples