Integrals Involving Aleph Function and Wright’s Generalized Hypergeometric Function

Abstract

Abstract. The aim of this paper is to establish certain integrals involving product of the Aleph function with Srivastava's polynomials and Fox-Wright's Generalized Hypergeometric function. Being unified and general in nature, these integrals yield a number of known and new results as special cases. For the sake of illustration, four corollaries are also recorded here as special case of our main results.

Certain Finite Integrals Related to the Products of Special Functions

“…Therefore, some suitable adjustments of the parameters of multivariable Aleph-functions and the general class of polynomials make it possible to obtain various other special functions (such as the I-function, the Fox H-function, Meijer's G-function, etc. ; see, e.g., [6]) involving a large variety of polynomials. Some of the issues of the main theorem have been already discussed here as special cases in the form of corollaries; they lead to significant applications in physics and engineering sciences.…”

“…The notation and complete definition in terms of the Mellin-Barnes-type integrals along with the conditions of convergence were presented by Saxena and Pogáany [2]. Later on, several studies were performed that established relationships between Aleph-functions with various fractional integral operators [3][4][5][6]. In addition, the multivariable Aleph-function is a generalization of the multivariable I-function defined by Sharma and Ahmad [7], which is itself a generalization of the multivariable H-function defined by Srivastava and Panda [8,9].…”

“…For more details, the reader may refer to the recent works of Ayant [10] and Suthar [6], in particular, as concerns the criteria for the absolute convergence of the above multiple Mellin-Barnes contour integral. They can be obtained by extending the corresponding conditions fulfilled by the multivariable H-function and are given by the conditions:…”

Exploring multi-index functions with significance relations and associated with general properties in fractional calculus

“…Edward Maitland Wright [46] established the generalized version of Bessel function, named Bessel-Maitland function. In [41,42], Suthar et al discussed certain properties of Bessel-Maitland function and further some extensions of Bessel-Maitland function also discussed in [8,38] for z, η ∈ C, α > 0 as…”

Estimates for Coefficients of Bi-Univalent Functions Associated with a Fractional q-Difference Operator

“…Srivastava et al [24] studied q-Noor integral operators and some of their applications. The q-calculus theory in a fractional sense and its real applications in the geometric class of functions of complex analysis and related fields are investigated in [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41].…”