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`

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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

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

See also