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2015•DergiPark (Istanbul University)Requires access

A generalization of the extended Jacobi polynomials in two variables

Rabıa Aktaş, Esra Erkuş-Duman

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Abstract

The main object of this paper is to construct a two-variable analogue of extended Jacobi polynomials and to give some properties of these polynomials. We obtain various differential formulae for two-variable extended Jacobi polynomials and give recurrence relations involving these polynomials. We derive various families of bilinear and bilateral generating functions. Furthermore, some special cases of the results are presented in this study.

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What this paper is about

The main object of this paper is to construct a two-variable analogue of extended Jacobi polynomials and to give some properties of these polynomials. We obtain various differential formulae for two-variable extended Jacobi polynomials and give recurrence relations involving these polynomials. We derive various families of bilinear and bilateral generating functions. Furthermore, some special cases of the results are presented in this study.

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Available abstract

The main object of this paper is to construct a two-variable analogue of extended Jacobi polynomials and to give some properties of these polynomials. We obtain various differential formulae for two-variable extended Jacobi polynomials and give recurrence relations involving these polynomials. We derive various families of bilinear and bilateral generating functions. Furthermore, some special cases of the results are presented in this study.

Key concepts: Jacobi polynomials, Mathematics, Generalization, Classical orthogonal polynomials, Difference polynomials, Variable (mathematics), Discrete orthogonal polynomials, Wilson polynomials

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