Local identities involving Jacobi elliptic functions View Full Text


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Article Info

DATE

2004-06

AUTHORS

Avinash Khare, Arul Lakshminarayan, Uday Sukhatme

ABSTRACT

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. More... »

PAGES

1201-1229

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf02704435

DOI

http://dx.doi.org/10.1007/bf02704435

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1036838468


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