Connecting Jacobi elliptic functions with different modulus parameters

Khare, Avinash ; Sukhatme, Uday (2004) Connecting Jacobi elliptic functions with different modulus parameters Pramana - Journal of Physics, 63 (5). pp. 921-936. ISSN 0304-4289

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Official URL: http://www.ias.ac.in/pramana/v63/p921/fulltext.pdf

Related URL: http://dx.doi.org/10.1007/BF02704331

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.

Item Type:Article
Source:Copyright of this article belongs to Indian Academy of Sciences.
Keywords:Landen Transformations; Jacobi Elliptic Functions; Cyclic Identities
ID Code:83280
Deposited On:20 Feb 2012 06:29
Last Modified:19 May 2016 00:11

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