The Euler transform of V-function

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].…”

On the generalized fractional Laplace transform

“…Definition 1.5. The author introduced a general class of functions defined in the following manner [13] (see also [14,15,19,20]):…”

“…For details of convergence conditions of the series on the right hand side of (1.10) one may refer to the paper [14].…”

Unified integral associated with the generalized V-function

“…For further information on the constraints of the convergence of the RHS of the series (1.1), we refer to Refs. [15,16]. The V-function defined by (1.1) is of general character as it assimilates a variety of valuable functions such as the Macrobert E-function, the exponential function [4], the generalized Mittag-Leffler function [9,23,31,34], the Lommel function [8], the Struve function [26,33,35], the generalized Bessel function [27], the Bessel function [5,36], the generalized hypergeometric function [4,32,37,38] and the unified Riemann-Zeta function [7].…”