Unified integral associated with the generalized V-function

Abstract

In this paper, we present two new unified integral formulas involving a generalized V-function. Some interesting special cases of the main results are also considered in the form of corollaries. Due to the general nature of the V-function, several results involving different special functions such as the exponential function, the Mittag-Leffler function, the Lommel function, the Struve function, the Wright generalized Bessel function, the Bessel function and the generalized hypergeometric function are obtained by specializing the parameters in the presented formulas. More results are also discussed in detail.

The Marichev-Saigo-Maeda Fractional Calculus Operators Pertaining to the V -Function

“…For descriptions of the series convergence constraints on (1) RHS, simply review [7][8][9][10]. The V-function defined by (1) is of a general character since it assimilates and applies a variety of valuable functions such as Macrobert's E-function and the exponential function [11], the generalized Mittag-Leffler function [12][13][14][15], Lommel's function [16], Struve's function [17][18][19][20][21], the Wright generalized Bessel function and the Bessel function [22][23][24][25], the generalized hypergeometric function [11,26], and the unified Riemann-Zeta function [27].…”