Contiguous Function Relations and an Integral Representation for Appell k-Series F_(1,k)

Abstract

The main objective of this paper is to derive contiguous function relations or recurrence relations and obtainan integral representation Appell -series , where .Keywords: Pochhammer -symbol, -gamma function, -beta function, Contiguous functions, Appell -series. Contribution/ OriginalityThis study originates a new formula for Appell's series in the form of a new symbol and contributes for deriving contiguous function relations, obtaining an integral representation of the Appell's series in terms of said symbol .

On Some Formulas for the k-Analogue of Appell Functions and Generating Relations via k-Fractional Derivative

“…Therefore, our study is generally based on the k-extension of hypergeometric functions. The structure of the paper is organized as follows: In Section 2, we briefly give some definitions and preliminary results which are essential in the following sections as noted in [13,23,26]. In Section 3, following [13,26] and using the same notion, we are concerned with the k-generalizations of F 2 and F 3 Appell hypergeometric functions.…”

“…The structure of the paper is organized as follows: In Section 2, we briefly give some definitions and preliminary results which are essential in the following sections as noted in [13,23,26]. In Section 3, following [13,26] and using the same notion, we are concerned with the k-generalizations of F 2 and F 3 Appell hypergeometric functions. Moreover, we prove some main properties such as integral representations, transformation formulas, and some reduction formulas which enable us to have relations for k-hypergeometric functions and k-Appell functions.…”

k-Fractional Estimates of Hermite–Hadamard Type Inequalities Involving k-Appell’s Hypergeometric Functions and Applications

“…For some more details, see [5]. The motivation of this paper is to obtain certain new k-fractional estimates of inequalities of Hermite-Hadamard type via s-convex functions of Breckner type essentially involving k-Appell's hypergeometric functions.…”

On Generalized k-Fractional Derivative Operator

“…The solution of some integral equations involving confluent k-hypergeometric functions and k-analogue of Kummer's first formula are given in [12,13]. While the k-hypergeometric and confluent k-hypergeometric differential equations are introduced in [10].…”