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

This paper aims to obtain the ξΨη-extended Whittaker function and its integral representations. This function is defined by using the ξΨη-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.