Generalized Wright Function and Its Properties Using Extended Beta Function

Abstract. In this paper, we introduce a new generalization of the Wright function by using an extended beta function and study some classical properties of this function. We establish several formulas involving integral transforms (e.g. Jacobi transform, Gegenbauer transform) and the generalized family of Wright function that does not seem to be reported in the literature even for the basic Wright function. Furthermore, we discuss other results including the recurrence relation, derivative formula, fractional derivative formula and also a partly bilateral and partly unilateral generating relation for the generalized Wright function.