Local identities involving Jacobi elliptic functions
نویسندگان
چکیده
منابع مشابه
Local Identities Involving Jacobi Elliptic Functions
We derive a number of local identities of arbitrary rank 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 of arbitrary rank. Second, we obtain a generalization to cyclic identities in which successive ter...
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We state and discuss numerous mathematical identities involving Jacobi elliptic functions sn (x,m), cn (x,m), dn (x,m), where m is the elliptic modulus parameter. In all identities, the arguments of the Jacobi functions are separated by either 2K(m)/p or 4K(m)/p, where p is an integer and K(m) is the complete elliptic integral of the first kind. Each p-point identity of rank r involves a cyclic...
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Abstract: Identities involving cyclic sums of terms composed from Jacobi elliptic functions evaluated at p equally shifted points on the real axis were recently found. These identities played a crucial role in discovering linear superposition solutions of a large number of important nonlinear equations. We derive four master identities, from which the identities discussed earlier are derivable ...
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Identities involving cyclic sums of terms composed from Jacobi elliptic functions evaluated at p equally shifted points were recently found. The purpose of this paper is to re-express these cyclic identities in terms of ratios of Jacobi theta functions, since many physicists prefer using Jacobi theta functions rather than Jacobi elliptic functions.
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ژورنال
عنوان ژورنال: Pramana
سال: 2004
ISSN: 0304-4289,0973-7111
DOI: 10.1007/bf02704435