elliptic_PI

Evaluate the incomplete elliptic integral of the third kind.

Evaluation of the Carlson elliptic integrals and the
incomplete elliptic integrals with complex arguments. The
implementations use Carlson's algorithms <doi:10.1007/BF02198293>.
Applications of elliptic integrals include probability distributions,
geometry, physics, mechanics, electrodynamics, statistical mechanics,
astronomy, geodesy, geodesics on conics, and magnetic field
calculations.

Stc3<a9>phane Laurent

Carlson

Carlson Elliptic Integrals and Incomplete Elliptic Integrals

elliptic_PI function

<dl><dt>phi</dt>
<dd>amplitude, real or complex number/vector</dd>
<dt>n</dt>
<dd>characteristic, real or complex number/vector</dd>
<dt>m</dt>
<dd>parameter, real or complex number/vector</dd>
<dt>minerror</dt>
<dd>the bound on the relative error passed to
<code>Carlson_RF</code> and <code>Carlson_RJ</code></dd></dl>

Arguments

Incomplete elliptic integral of the third kind — elliptic_PI

<dl>

<dt>phi</dt>
<dd>amplitude, real or complex number/vector</dd>


<dt>n</dt>
<dd>characteristic, real or complex number/vector</dd>


<dt>m</dt>
<dd>parameter, real or complex number/vector</dd>


<dt>minerror</dt>
<dd>the bound on the relative error passed to
<code>Carlson_RF</code> and <code>Carlson_RJ</code></dd>

</dl>

elliptic_PI: Incomplete elliptic integral of the third kind

Description

Usage

Value

Arguments

Examples