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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/09.29.18.0075.01









  


  










Input Form





JacobiDN[z, m] JacobiDN[z + a, m] JacobiDN[z + b, m] JacobiDN[z + c, m] == (-JacobiCS[a, m]) JacobiCS[b, m] (JacobiDN[c, m] + JacobiCS[c, m] (JacobiZeta[JacobiAmplitude[z + c, m], m] - JacobiZeta[JacobiAmplitude[z, m], m] - JacobiZeta[JacobiAmplitude[c, m], m])) - JacobiCS[a, m] JacobiCS[a - b, m] (JacobiDN[c - a, m] + JacobiCS[c - a, m] (JacobiZeta[JacobiAmplitude[z + c, m], m] - JacobiZeta[JacobiAmplitude[z + a, m], m] - JacobiZeta[JacobiAmplitude[c - a, m], m])) - JacobiCS[b, m] JacobiCS[a - b, m] (JacobiDN[c - b, m] + JacobiCS[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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</cn> <ci> b </ci> </apply> </apply> <ci> m </ci> </apply> <apply> <plus /> <apply> <ci> JacobiDN </ci> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> <ci> m </ci> </apply> <apply> <times /> <apply> <ci> JacobiCS </ci> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> <ci> m </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> JacobiZeta </ci> <apply> <ci> JacobiAmplitude </ci> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> <ci> m </ci> </apply> <ci> m </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> JacobiZeta </ci> <apply> <ci> JacobiAmplitude </ci> <apply> <plus /> <ci> a </ci> <ci> z </ci> </apply> <ci> m </ci> </apply> <ci> m </ci> </apply> </apply> <apply> <ci> JacobiZeta </ci> <apply> <ci> JacobiAmplitude </ci> <apply> <plus /> 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</apply> </apply> <apply> <ci> JacobiZeta </ci> <apply> <ci> JacobiAmplitude </ci> <apply> <plus /> <ci> c </ci> <ci> z </ci> </apply> <ci> m </ci> </apply> <ci> m </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> JacobiZeta </ci> <apply> <ci> JacobiAmplitude </ci> <ci> z </ci> <ci> m </ci> </apply> <ci> m </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










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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