Local identities involving Jacobi elliptic functions

Khare, Avinash ; Lakshminarayan, Arul ; Sukhatme, Uday (2004) Local identities involving Jacobi elliptic functions Pramana - Journal of Physics, 62 (6). pp. 1201-1229. ISSN 0304-4289

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Official URL: http://www.ias.ac.in/pramana/v62/p1201/fulltext.pd...

Related URL: http://dx.doi.org/10.1007/BF02704435


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), wheres is any integer. Third, we systematize the local identities by deriving four local 'master identities' analogous to the master identities for the cyclic sums discussed by us previously. Fourth, we point out that many of the local identities can be thought of as exact discretizations of standard non-linear differential equations satisfied by the Jacobi elliptic functions. Finally, we obtain explicit answers for a number of definite integrals and simpler forms for several indefinite integrals involving Jacobi elliptic functions.

Item Type:Article
Source:Copyright of this article belongs to Indian Academy of Sciences.
Keywords:Jacobi Elliptic Functions; Cyclic Identities; Local Identities
ID Code:83279
Deposited On:20 Feb 2012 06:29
Last Modified:19 May 2016 00:11

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