Articles written in Pramana – Journal of Physics
Volume 62 Issue 6 June 2004 pp 1201-1229
We derive a number of local identities involving Jacobi elliptic functions and use them to obtain several new results. First, we present an alternative, simpler derivation of the cyclic identities discovered by us recently, along with an extension to several new cyclic identities. Second, we obtain a generalization to cyclic identities in which successive terms have a multiplicative phase factor exp(2iπ/s), where
Volume 63 Issue 5 November 2004 pp 921-936
The simplest formulas connecting Jacobi elliptic functions with different modulus parameters were first obtained over two hundred years ago by John Landen. His approach was to change integration variables in elliptic integrals. We show that Landen’s formulas and their subsequent generalizations can also be obtained from a different approach, using which we also obtain several new Landen transformations. Our new method is based on recently obtained periodic solutions of physically interesting non-linear differential equations and remarkable new cyclic identities involving Jacobi elliptic functions.
Volume 96, 2022
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