Jacobi zeta function: Representations through more general functions (formula 08.07.26.0001)

JacobiZeta

$Mathematica Notation$

Elliptic Integrals

JacobiZeta[z,m]

Representations through more general functions

Through hypergeometric functions of two variables

http://functions.wolfram.com/08.07.26.0001.01

Input Form

JacobiZeta[z, m] == EllipticE[m] - Cos[z] (HypergeometricPFQ[{{1/2}, {-(1/2), 1/2}, {1/2, 1}}, {{1, 3/2}, {}, {}}, (-m) Cos[z]^2, Cos[z]^2] - (m/2) HypergeometricPFQ[{{1/2, 3/2}, {1/2}, {1}}, {{2}, {3/2}, {3/2}}, (-m) Cos[z]^2, m]) - (EllipticE[m]/EllipticK[m]) Sin[z] HypergeometricPFQ[{{1/2}, {1/2}, {1/2}}, {{3/2}, {}, {}}, m Sin[z]^2, Sin[z]^2]

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2001-10-29