Certain Integral and Differential Formulas Involving the Product of Srivastava’s Polynomials and Extended Wright Function

Abstract

Many authors have established various integral and differential formulas involving different special functions in recent years. In continuation, we explore some image formulas associated with the product of Srivastava’s polynomials and extended Wright function by using Marichev–Saigo–Maeda fractional integral and differential operators, Lavoie–Trottier and Oberhettinger integral operators. The obtained outcomes are in the form of the Fox–Wright function. It is worth mentioning that some interesting special cases are also discussed.

More on the Unified Mittag–Leffler Function

“…The extensions of Mittag-Leffler function is an interesting topic for researchers in which the classical notions linked with predefined Mittag-Leffler functions are investigated in more general prospect, see [9][10][11]. The Wright function is the generalization of hypergeometric function and several other special functions based on the gamma function, see [12][13][14][15]. The extensions of Mittag-Leffler function which are due to the gamma function can be obtained from the Wright function.…”

“…Proof. In (13) writing the Wright generalized function in terms of Mellin-Barnes integral by using (11), one can have (15).…”

On the Composition Structures of Certain Fractional Integral Operators

“…Saigo's operators involve the Gauss hypergeometric functions 2 F 1 as kernels and possess many properties (see, for example, Refs. [1][2][3][4][5]). Over the past few decades, Saigo's operators have been applied in various branches of mathematics, especially in the Geometric Function Theory (see Refs.…”