Symbolic Computation of Elliptic Rational Functions
ABSTRACT Elliptic rational functions have been traditionally derived from the Jacobi elliptic functions that are computationaly intensive. In this paper we construct the elliptic rational function, in the closed form, bypassing mathematical theory of special functions. We build the knowledge of the elliptic rational function using simple algebraic manipulations, only. A nesting property of elliptic rational functions is presented. I. Introduction The design of elliptic-function filters is based on the elliptic rational function (ERF), which has been traditionally derived from the Jacobi elliptic functions. In this paper we introduce the elliptic rational function as a natural generalization of the Chebyshev polynomial and we bypass mathematical theory of special functions required by the classical filter theory. Our goal is to build the knowledge of the elliptic rational function using simple algebraic manipulations, even, without mentioning the Jacobi elliptic functions. II. Second-order Ell...