# Incomplete elliptic integral of 3d kind `Pi(phi,k,n)`

`Pi(phi,k,n) = \int_0^phi \ (d theta)/((1-n*sin^2 theta)*(sqrt(1-k^2*sin^2 theta)))` `-1<=k<=1`

This tool is a calculator of incomplete elliptic integral of third kind.

`Pi(phi,k,n) = \int_0^phi \ (d theta)/((1-n*sin^2 theta)*(sqrt(1-k^2*sin^2 theta)))`

`phi` : amplitude

k : module or eccentricity ( -1 <= k <= 1)

n : characteristic

Incomplete elliptic integral of third kind (x)

## See also

### Incomplete Integral Calculators

incomplete elliptic integral of first kind (`phi`)incomplete elliptic integral of first kind (`x`)

incomplete elliptic integral of second kind (`phi`)

incomplete elliptic integral of second kind (`x`)

### Complete Integral Calculators

Complete elliptic integral of first kindComplete elliptic integral of second kind

Complete elliptic integral of third kind

### Other Calculators

Special functions Calculators

Mathématics Calculators