On the Laplace Transforms of Derivatives of Special Functions with Respect to Parameters

Abstract

This article is devoted to the derivation of the Laplace transforms of the derivatives with respect to parameters of certain special functions, namely, the Mittag–Leffler-type, Wright, and Le Roy-type functions. These formulas show the interconnection of these functions and lead to a better understanding of their behavior on the real line. These formulas are represented in a convoluted form and reconstructed in a more suitable form by using the Efros theorem.