Cyclic Identities Involving Jacobi Elliptic Functions. II

Details Cyclic Identities Involving Jacobi Elliptic Functions. II Cyclic Identities Involving Jacobi Elliptic Functions. II

2002-07-15

arxiv.org/abs/math-ph/0207019v2

J. Math. Phys., Vol. 44, No. 4 (2003) 1822-1841.

Physics

Mathematical Physics

38 pages. Modified and includes more new identities. A shorter version of this will appear in J. Math. Phys. (May 2003)

Scientific paper

10.1063/1.1560856

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.

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