Jacobi elliptic function dn: Identities involving the group of functions (formula 09.29.18.0086)

JacobiDN

$Mathematica Notation$

Elliptic Functions

JacobiDN[z,m]

Identities involving the group of functions

Local identities of rank 4

Rank 4 identities with 4 distinct arguments

http://functions.wolfram.com/09.29.18.0086.01

Input Form

m^2 JacobiSN[z, m] JacobiCN[z + a, m] JacobiCN[z + b, m] JacobiSN[z + c, m] == JacobiDS[a, m] JacobiDS[b, m] JacobiNS[c, m] (JacobiZeta[JacobiAmplitude[z + c, m], m] - JacobiZeta[JacobiAmplitude[z, m], m] - JacobiZeta[JacobiAmplitude[c, m], m]) + JacobiNS[a, m] JacobiDS[a - b, m] JacobiNS[c - a, m] (JacobiZeta[JacobiAmplitude[z + c, m], m] - JacobiZeta[JacobiAmplitude[z + a, m], m] - JacobiZeta[JacobiAmplitude[c - a, m], m]) - JacobiNS[b, m] JacobiDS[a - b, m] JacobiNS[c - b, m] (JacobiZeta[JacobiAmplitude[z + c, m], m] - JacobiZeta[JacobiAmplitude[z + b, m], m] - JacobiZeta[JacobiAmplitude[c - b, m], m])

Standard Form

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MathML Form

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Rule Form

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References

A. Khare, A. Lakshminarayan, U. Sukhatme, "Local Identities Involving Jacobi Elliptic Functions", math-ph/0306028, (2003) http://arXiv.org/abs/math-ph/0306028

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

2003-08-21