On the Laplace transforms of derivatives of special functions with respect to parameters

TL;DR

This paper derives Laplace transforms of parameter derivatives of special functions like Mittag-Leffler, Wright, and Le Roy types, revealing their interconnections and enhancing understanding of their behavior through convoluted and reformulated expressions.

Contribution

It provides new formulas for the Laplace transforms of derivatives of key special functions, utilizing Efros theorem for better analytical insight.

Findings

Derived explicit Laplace transform formulas for derivatives of special functions.

Revealed interconnections among Mittag-Leffler, Wright, and Le Roy functions.

Enhanced understanding of the functions' behavior on the real line.

Abstract

This article is devoted to 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 interconnection of these functions and lead to better understanding of their behaviour on the real line. These formulas are represented in the convoluted form and reconstructed in a more suitable form by using Efros theorem