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    • Connecting Jacobi elliptic functions with different modulus parameters

      Avinash Khare Uday Sukhatme

      Volume 63 Issue 5 November 2004 pp 921-936

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pram/063/05/0921-0936

    • Keywords

       

      Landen transformations; Jacobi elliptic functions; cyclic identities

    • Abstract

       

      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.

    • Author Affiliations

       

      Avinash Khare1 Uday Sukhatme2

      1. Institute of Physics, Sachivalaya Marg, Bhubaneswar - 751 005, India
      2. Department of Physics, State University of New York at Buffalo, Buffalo, New York - 14260, USA

    • Dates

       
      Published
      November 2004
      Manuscript received
      13 April 2004
      Accepted
      31 July 2004

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