Inverse of the Jacobi elliptic function dn: Representations through equivalent functions (formula 09.41.27.0018)

InverseJacobiDN

$Mathematica Notation$

Elliptic Functions

InverseJacobiDN[z,m]

Representations through equivalent functions

With related functions

Involving elliptic integrals

http://functions.wolfram.com/09.41.27.0018.01

Input Form

InverseJacobiDN[z, m] == ((Sqrt[1 - z^2] JacobiCS[InverseJacobiDN[z, m], m])/ Sqrt[-1 + m + z^2]) ((-(1/Sqrt[-1 + m + z^2])) Sqrt[(-1 + m + z^2)/(-1 + m)] EllipticF[ArcSin[z], 1/(1 - m)] + (1/Sqrt[m]) Sqrt[m/(-1 + m)] EllipticK[1/(1 - m)]) /; !Exists[\[Tau], {Element[\[Tau], Reals], 0 < \[Tau] < 1}, Im[1 - (1 + \[Tau] (z - 1))^2] == 0 && 1 - (1 + \[Tau] (z - 1))^2 < 0 && Im[(1 + \[Tau] (z - 1))^2 + m - 1] == 0 && (1 + \[Tau] (z - 1))^2 + m - 1 < 0]

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)

2007-05-02