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JacobiCN






Mathematica Notation

Traditional Notation









Elliptic Functions > JacobiCN[z,m] > Transformations > Sums over products of three Jacobi functions





http://functions.wolfram.com/09.26.16.0077.01









  


  










Input Form





Sum[JacobiSN[z + 4 k (EllipticK[m]/p), m] (JacobiCN[z + 4 (k + r) (EllipticK[m]/p), m] JacobiCN[z + 4 (k + s) (EllipticK[m]/p), m] + JacobiCN[z + 4 (k - r) (EllipticK[m]/p), m] JacobiCN[z + 4 (k - s) (EllipticK[m]/p), m]), {k, 0, p - 1}] == (-(2/m)) (JacobiDS[4 r (EllipticK[m]/p), m] JacobiDS[4 s (EllipticK[m]/p), m] + JacobiDS[4 (r - s) (EllipticK[m]/p), m] (JacobiNS[4 r (EllipticK[m]/p), m] - JacobiNS[4 s (EllipticK[m]/p), m])) Sum[JacobiSN[z + 4 k (EllipticK[m]/p), m], {k, 0, p - 1}] /; Element[p, Integers] && p >= 1 && Element[r, Integers] && Inequality[1, LessEqual, r, Less, p] && Element[s, Integers] && Inequality[1, LessEqual, s, Less, r]










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, "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)










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





2002-12-18





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