Communications of the
Korean Mathematical Society CKMS

The main aim of this paper is to introduce a new generalization of the Wright series in two variables, which is expressed in terms of Hermite polynomials. The properties of the freshly defined function involving its auxiliary functions and the integral representations are established. Furthermore, a Gauss-Hermite quadrature and Gaussian quadrature formulas have been established to evaluate some integral representations of our main results and compare them with our theoretical evaluations using graphical simulations.

Keywords: Generalization of the Wright series, Hermite polynomials, auxiliary functions

MSC numbers: Primary 33B15, 33C10, 33C15