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 Rc function.

carlson-rd

Carlson's Rd function.

carlson-rf

Carlson's Rf function.

carlson-rj

Carlson's Rj function.

References

• ​DLMF Elliptic Integrals