On the Whittaker Function Extended by the Fox-Wright Function and Its Properties

Abstract

This paper aims to obtain the Psi eta xi-extended Whittaker function and its integral representations. This function is defined by using the Psi eta xi-confluent hypergeometric function, which was recently extended in terms of the Fox-Wright function. Furthermore, we discuss properties including a transformation formula, integral transforms (Laplace-Mellin and Hankel transforms), and a differential formula. Our results provide a unified framework for several known generalizations of the Whittaker function and highlight potential applications in applied mathematics and theoretical physics.