wiki:EllipticIntegrals

Version 4 (modified by rtoy, 4 years ago) (diff)

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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