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

`Pi(x,k,n) = \int_0^x \ (dt)/((1-n*t^2)*(sqrt((1-t^2)(1-k^2*t^2)))` `-1<=k<=1` and `-1<=x<=1`

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

`Pi(x,k,n) = \int_0^x \ (dt)/((1-n*t^2)*(sqrt((1-t^2)(1-k^2*t^2)))`

x : parameter ( -1 <= x <= 1)

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

n : characteristic

By substituting `x = sin(phi)` and `t = sin(theta)`, we obtain another form of the same function :

Incomplete elliptic integral of third kind (`phi`)

## See also

### Incomplete Integral Calculators

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

incomplete elliptic integral of first kind (`phi`)

incomplete elliptic integral of first 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