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`

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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