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JacobiDN






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/09.29.16.0110.01









  


  










Input Form





Sum[(-1)^k JacobiSN[z + 2 k (EllipticK[m]/p), m] (JacobiDN[z + 2 (k + r) (EllipticK[m]/p), m] JacobiSN[z + 2 (k + r) (EllipticK[m]/p), m] + JacobiDN[z + 2 (k - r) (EllipticK[m]/p), m] JacobiSN[z + 2 (k - r) (EllipticK[m]/p), m]), {k, 0, p - 1}] == (2/m) JacobiCS[2 r (EllipticK[m]/p), m] (JacobiNS[2 r (EllipticK[m]/p), m] + JacobiDS[2 r (EllipticK[m]/p), m]) Sum[(-1)^k JacobiDN[z + 2 k (EllipticK[m]/p), m], {k, 0, p - 1}] /; Element[p/2, Integers] && p >= 2 && Element[r, Integers] && r >= 1 && GCD[p, r] == 1










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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