kleinj

kleinjinv

Evaluation of the Klein j-invariant function and its inverse.

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

kleinj function

<dl><dt>tau</dt>
<dd>a complex number with strictly positive imaginary part, or a 
vector or matrix of such complex numbers; missing values allowed</dd>
<dt>transfo</dt>
<dd>Boolean, whether to use a transformation of the values
of <code>tau</code> close to the real line; using this option can fix some 
failures of the computation (at the cost of speed), e.g. when the 
algorithm reaches the maximal number of iterations</dd>
<dt>j</dt>
<dd>a complex number</dd></dl>

Arguments

Klein j-function and its inverse — kleinj

<dl>

<dt>tau</dt>
<dd>a complex number with strictly positive imaginary part, or a 
vector or matrix of such complex numbers; missing values allowed</dd>


<dt>transfo</dt>
<dd>Boolean, whether to use a transformation of the values
of <code>tau</code> close to the real line; using this option can fix some 
failures of the computation (at the cost of speed), e.g. when the 
algorithm reaches the maximal number of iterations</dd>


<dt>j</dt>
<dd>a complex number</dd>

</dl>

kleinj: Klein j-function and its inverse

Description

Usage

Value

Arguments

Examples