Elliptic Integrals

With careful standardization of argument conventions, Mathematica provides full coverage of elliptic integrals, with arbitrary-precision numerical evaluation for complex values of all parameters, as well as extensive symbolic transformations and simplifications.

ReferenceReference

EllipticK complete elliptic integral of the first kind

EllipticF incomplete elliptic integral of the first kind

EllipticE complete and incomplete elliptic integral of the second kind

EllipticPi complete and incomplete elliptic integral of the third kind

JacobiZeta ▪ EllipticLog ▪ ArithmeticGeometricMean ▪ InverseWeierstrassP

EllipticNomeQ convert from parameter m to nome q

InverseEllipticNomeQ convert from nome q to parameter m

JacobiAmplitude convert from argument u and parameter m to amplitude

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