Abstract
Recently, many extensions of some special functions are defined by using the extended Beta function. In this paper, we introduce a new generalization of extended Gegenbauer polynomials of two variables by using the extended Gamma function. Some properties of these generalized polynomials such as integral representation, recurrence relation and generating functions are obtained.
Highlights
Recently, many extensions of some special functions are defined by using the extended Beta function
We introduce a new generalization of extended Gegenbauer polynomials of two variables by using the extended Gamma function
I n recent years, several extensions of the well known special functions have been considered by several authors [1–5]
Summary
I n recent years, several extensions of the well known special functions have been considered by several authors [1–5]. In terms of the extended Gamma function Γ(a,p)(x) defined in (4), we introduce a new generalization of extended Gegenbauer polynomials of two variables , denoted by Cnα(x, y; a, p), as follows:
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