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Complete Elliptic Integral of the Third Kind

EllipticPi

The complete elliptic integral of the third kind Pi(n|m) is defined in terms of the incomplete elliptic integral of the third kind Pi(n;phi|m) by

Pi(n|m)=Pi(n;1/2pi|m)

where n is a constant known as the elliptic characteristic, m=k^2 is the parameter, and k is the elliptic modulus.

It is implemented in the Wolfram Language as EllipticPi[n, m].

See also

Complete Elliptic Integral of the First Kind, Complete Elliptic Integral of the Second Kind, Elliptic Integral of the Third Kind

Related Wolfram sites

http://functions.wolfram.com/EllipticIntegrals/EllipticPi3/

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Cite this as:

Weisstein, Eric W. "Complete Elliptic Integral of the Third Kind." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CompleteEllipticIntegraloftheThirdKind.html

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