Jacobi elliptic function dn: Transformations (formula 09.29.16.0054)

JacobiDN

$Mathematica Notation$

Elliptic Functions

JacobiDN[z,m]

Transformations

Sums over products of three Jacobi functions

http://functions.wolfram.com/09.29.16.0054.01

Input Form

JacobiDN[z, m]^2 JacobiDN[z + EllipticK[m], m] + JacobiDN[z + EllipticK[m]/2, m]^2 JacobiDN[z + (3 EllipticK[m])/2, m] + JacobiDN[z + EllipticK[m], m]^2 JacobiDN[z, m] + JacobiDN[z + (3 EllipticK[m])/2, m]^2 JacobiDN[z + EllipticK[m]/2, m] == Sqrt[1 - m] (JacobiDN[z, m] + JacobiDN[z + EllipticK[m]/2, m] + JacobiDN[z + EllipticK[m], m] + JacobiDN[z + (3 EllipticK[m])/2, m])

Standard Form

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MathML Form

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Rule Form

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References

A. Khare, U. Sukhatme, "Cyclic Identities Involving Jacobi Elliptic Functions", math-ph/0201004, (2002) http://arXiv.org/abs/math-ph/0201004

A. Khare, U. Sukhatme, "Cyclic Identities Involving Jacobi Elliptic Functions", Journal of Mathematical Physics, v. 43, issue 7, pp. 3798-3806 (2002)

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

2002-03-07