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JacobiDN






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/09.29.16.0117.01









  


  










Input Form





Sum[JacobiDN[z + 2 k (EllipticK[m]/p), m]^2 JacobiDN[z + 2 (k + r) (EllipticK[m]/p), m]^2, {k, 0, p - 1}] == -2 JacobiCS[2 r (EllipticK[m]/p), m]^2 Sum[JacobiDN[z + 2 k (EllipticK[m]/p), m]^2, {k, 0, p - 1}] + (p/(2 EllipticK[m])) (Integrate[JacobiDN[t, m]^2 JacobiDN[t + 2 r (EllipticK[m]/p), m]^2, {t, 0, 2 EllipticK[m]}] + 4 EllipticE[m] JacobiCS[2 r (EllipticK[m]/p), m]^2) /; Element[p, Integers] && p >= 1 && Element[r, Integers] && Inequality[1, LessEqual, r, Less, p - 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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