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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 R_{c} function.
- carlson-rd
- Carlson's R_{d} function.
- carlson-rf
- Carlson's R_{f} function.
- carlson-rj
- Carlson's R_{j} function.