## complete

the complete elliptic integral of the first kind

`elliptic_k(m)`

`elliptic_k2(m) == elliptic_k(m^2)`

the complete elliptic integral of the second kind

`elliptic_e(m)`

`elliptic_e2(m) == elliptic_e(m^2)`

the complete elliptic integral of the third kind

`elliptic_pi(n, m)`

`elliptic_pi2(n, m) == elliptic_pi(n, m^2)`

## incomplete

the incomplete elliptic integral of the first kind

`elliptic_f(phi, m)`

`elliptic_f2(phi, m) == elliptic_f(phi, m^2)`

the incomplete elliptic integral of the second kind

`elliptic_e(phi, m)`

`elliptic_e2(phi, m) == elliptic_e(phi, m^2)`

the incomplete elliptic integral of the third kind

`elliptic_pi(n, phi, m)`

`elliptic_pi2(n, phi, m) == elliptic_pi(n, phi, m^2)`

## symmetric (Carlson)

- the symmetric elliptic integral of the first kind
`elliptic_rf(x, y, z)`

- the symmetric elliptic integral of the second kind
`elliptic_rg(x, y, z)`

- the symmetric elliptic integral of the third kind
`elliptic_rj(x, y, z)`