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 KindRelated Wolfram sites
https://functions.wolfram.com/EllipticIntegrals/EllipticPi3/Explore with Wolfram|Alpha
WolframAlpha
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Cite this as:
Weisstein, Eric W. "Complete Elliptic Integral of the Third Kind." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CompleteEllipticIntegraloftheThirdKind.html