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)

elliptic-k

Complete elliptic integral of the first kind.

elliptic-f

Incomplete elliptic integral of the first kind.

elliptic-ec

Complete elliptic integral of the second kind.

elliptic-e

Incomplete elliptic integral of the second kind.

elliptic-pi

Incomplete elliptic integral of the third kind.

Carlson Form

See  DLMF 19.16

carlson-rc

Carlson's R_c function.

carlson-rd

Carlson's R_d function.

carlson-rf

Carlson's R_f function.

carlson-rj

Carlson's R_j function.

References

•  DLMF Elliptic Integrals