Elliptic Integrals
Introduction
There are many different forms of elliptic integrals. In oct
,
we support Legendre's form and Carlson's symmetric form. For mre
details see DLMF Elliptic Integrals
For the Legendre integrals, all of the functions use the parameter m instead of the modular angle alpha or the modulus k.
Functions
The following complete and incomplete elliptic integrals are supported:
Legendre Form
See DLMF 19.2(ii)
 elliptick
 Complete elliptic integral of the first kind.
 ellipticf
 Incomplete elliptic integral of the first kind.
 ellipticec
 Complete elliptic integral of the second kind.
 elliptice
 Incomplete elliptic integral of the second kind.
 ellipticpi
 Incomplete elliptic integral of the third kind.
Carlson Form
See DLMF 19.16
 carlsonrc

Carlson's
R
_{c} function.  carlsonrd

Carlson's
R
_{d} function.  carlsonrf

Carlson's
R
_{f} function.  carlsonrj

Carlson's
R
_{j} function.
References
Last modified 12 years ago
Last modified on 03/15/11 13:54:40