A Unified Framework for Analytical Transforms of the Y-Function

Abstract: This paper explores the properties of the 𝑌-function using various important integral transforms. We evaluate and derive clear expressions for the Euler, Hankel, Whittaker, K-, and 𝑃𝛿 -transforms applied to the 𝑌-function kernel. Using the Mellin-Barnes integral representation, we show that the resulting images can be clearly expressed in terms of the original 𝑌-function and the generalized Fox-H function. These findings create new functional relations and broaden the existing techniques for hypergeometric-type functions.

Keywords: Y-function;Euler Transform;Mellin Transform;Laplace Transform;Whittaker transform; Hankel Transform