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JacobiDN






Mathematica Notation

Traditional Notation









Elliptic Functions > JacobiDN[z,m] > Identities involving the group of functions > Local identities of rank 4 > Rank 4 identities with 4 distinct arguments





http://functions.wolfram.com/09.29.18.0077.01









  


  










Input Form





m^2 JacobiCN[z, m] JacobiCN[z + a, m] JacobiCN[z + b, m] JacobiCN[z + c, m] == (-JacobiDS[a, m]) JacobiDS[b, m] (m JacobiCN[c, m] + JacobiDS[c, m] (JacobiZeta[JacobiAmplitude[z + c, m], m] - JacobiZeta[JacobiAmplitude[z, m], m] - JacobiZeta[JacobiAmplitude[c, m], m])) - JacobiDS[a, m] JacobiDS[a - b, m] (m JacobiCN[c - a, m] + JacobiDS[c - a, m] (JacobiZeta[JacobiAmplitude[z + c, m], m] - JacobiZeta[JacobiAmplitude[z + a, m], m] - JacobiZeta[JacobiAmplitude[c - a, m], m])) + JacobiDS[b, m] JacobiDS[a - b, m] (m JacobiCN[c - b, m] + JacobiDS[c - b, m] (JacobiZeta[JacobiAmplitude[z + c, m], m] - JacobiZeta[JacobiAmplitude[z + b, m], m] - JacobiZeta[JacobiAmplitude[c - b, m], m]))










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