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Zbl 1062.33020
Khare, Avinash; Lakshminarayan, Arul; Sukhatme, Uday
Cyclic identities for Jacobi elliptic and related functions. (English)
[J] J. Math. Phys. 44, No. 4, 1822-1841 (2003). ISSN 0022-2488; ISSN 1089-7658/e

Summary: Identities involving cyclic sums of terms composed from Jacobi elliptic functions evaluated at $p$ equally shifted points on the real axis were recently found. These identities played a crucial role in discovering linear superposition solutions of a large number of important nonlinear equations. We derive four master identities, from which the identities discussed earlier are derivable as special cases. Master identities are also obtained which lead to cyclic identities with alternating signs. We discuss an extension of our results to pure imaginary and complex shifts as well as to the ratio of Jacobi theta functions.

MSC 2000:: *33E05 Elliptic functions and integrals

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