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2005•Journal of Nonlinear Mathematical PhysicsOpen access

On Properties of Elliptic Jacobi Functions and Applications

A. Raouf Chouikha

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Abstract

In this paper we are interested in developments of the elliptic functions of Jacobi.In particular a trigonometric expansion of the classical theta functions introduced by the author (Algebraic methods and q-special functions, C.R.M. Proceedings and Lectures Notes, A.M.S., vol 22, Providence, 1999, 53-57) permits one to establish a differential system.This system is derived from the heat equation and is satisfied by their coefficients.Several applications may be deduced.Other types of expansions for the Jacobi elliptic functions as well as for the Zeta function are examined.

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In this paper we are interested in developments of the elliptic functions of Jacobi.In particular a trigonometric expansion of the classical theta functions introduced by the author (Algebraic methods and q-special functions, C.R.M. Proceedings and Lectures Notes, A.M.S., vol 22, Providence, 1999, 53-57) permits one to establish a differential system.This system is derived from the heat equation and is satisfied by their coefficients.Several applications may be deduced.Other types of expansions for the Jacobi elliptic functions as well as for the Zeta function are examined.

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Available abstract

In this paper we are interested in developments of the elliptic functions of Jacobi.In particular a trigonometric expansion of the classical theta functions introduced by the author (Algebraic methods and q-special functions, C.R.M. Proceedings and Lectures Notes, A.M.S., vol 22, Providence, 1999, 53-57) permits one to establish a differential system.This system is derived from the heat equation and is satisfied by their coefficients.Several applications may be deduced.Other types of expansions for the Jacobi elliptic functions as well as for the Zeta function are examined.

Key concepts: Jacobi elliptic functions, Elliptic function, Mathematics, Elliptic integral, Trigonometric functions, Quarter period, Elliptic rational functions, Trigonometry

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