Jacobi elliptic function dn: Transformations (formula 09.29.16.0069)

JacobiDN

$Mathematica Notation$

Elliptic Functions

JacobiDN[z,m]

Transformations

Sums over products of four Jacobi functions

http://functions.wolfram.com/09.29.16.0069.01

Input Form

JacobiDN[z, m]^3 (JacobiDN[z + (2 EllipticK[m])/3, m] + JacobiDN[z + (4 EllipticK[m])/3, m]) + JacobiDN[z + (2 EllipticK[m])/3, m]^3 (JacobiDN[z + (4 EllipticK[m])/3, m] + JacobiDN[z, m]) + JacobiDN[z + (4 EllipticK[m])/3, m]^3 (JacobiDN[z, m] + JacobiDN[z + (2 EllipticK[m])/3, m]) == ((2 m JacobiDN[(2 EllipticK[m])/3, m])/(1 - JacobiDN[(2 EllipticK[m])/3, m]^ 2)) (JacobiDN[z, m]^2 + JacobiDN[z + (2 EllipticK[m])/3, m]^2 + JacobiDN[z + (4 EllipticK[m])/3, m]^2) - 2 (1 - 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