Sum[Product[JacobiSN[z + 2 (j + k) (EllipticK[m]/p), m], {k, 0, r - 1}], {j, 0, p - 1}] == (p/(2 EllipticK[m])) Integrate[Product[JacobiSN[t + 2 k (EllipticK[m]/p), m], {k, 0, r - 1}], {t, 0, 2 EllipticK[m]}] /; Element[p, Integers] && p >= 3 && Element[r/2, Integers] && Inequality[2, LessEqual, r, Less, p - 1]

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A. Khare, A. Lakshminarayan, U. Sukhatme, "Cyclic Identities Involving Jacobi Elliptic Functions. II", math-ph/0207019, (2002) http://arXiv.org/abs/math-ph/0207019

A. Khare, A. Lakshminarayan, U. Sukhatme, "Cyclic Identities Involving Jacobi Elliptic Functions", Journal of Mathematical Physics, v. 44, issue 4, pp. 1822-1841 (2003)

2002-12-18