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JacobiDN






Mathematica Notation

Traditional Notation









Elliptic Functions > JacobiDN[z,m] > Identities involving the group of functions > Higher order local identities > Local identities of arbitrary rank





http://functions.wolfram.com/09.29.18.0146.01









  


  










Input Form





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










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, "Local Identities Involving Jacobi Elliptic Functions", math-ph/0306028, (2003) http://arXiv.org/abs/math-ph/0306028










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





2003-08-21





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