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

Sergei Rogosin, Filippo Giraldi and Francesco Mainardi ()
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Sergei Rogosin: Department of Economics, Belarusian State University, Nezavisimosti Ave. 4, 220030 Minsk, Belarus
Filippo Giraldi: Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II 39, 00186 Rome, Italy
Francesco Mainardi: Department of Physics & Astronomy, University of Bologna, and INFN, Via Irnerio 46, 40126 Bologna, Italy

Mathematics, 2025, vol. 13, issue 12, 1-14

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.

Keywords: Mittag–Leffler function; Le Roy-type function; differentiation; Laplace transforms; Efros theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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