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

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 understa...

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Main Authors: Sergei Rogosin, Filippo Giraldi, Francesco Mainardi
Format: Article
Language:English
Published: MDPI AG 2025-06-01
Series:Mathematics
Subjects:
Online Access:https://www.mdpi.com/2227-7390/13/12/1980
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author Sergei Rogosin
Filippo Giraldi
Francesco Mainardi
author_facet Sergei Rogosin
Filippo Giraldi
Francesco Mainardi
author_sort Sergei Rogosin
collection DOAJ
description 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.
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spelling doaj-art-f2e2491277344e4eae62c56c85418af22025-08-20T02:20:58ZengMDPI AGMathematics2227-73902025-06-011312198010.3390/math13121980On the Laplace Transforms of Derivatives of Special Functions with Respect to ParametersSergei Rogosin0Filippo Giraldi1Francesco Mainardi2Department of Economics, Belarusian State University, Nezavisimosti Ave. 4, 220030 Minsk, BelarusSection of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II 39, 00186 Rome, ItalyDepartment of Physics & Astronomy, University of Bologna, and INFN, Via Irnerio 46, 40126 Bologna, ItalyThis 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.https://www.mdpi.com/2227-7390/13/12/1980Mittag–Leffler functionLe Roy-type functiondifferentiationLaplace transformsEfros theorem
spellingShingle Sergei Rogosin
Filippo Giraldi
Francesco Mainardi
On the Laplace Transforms of Derivatives of Special Functions with Respect to Parameters
Mathematics
Mittag–Leffler function
Le Roy-type function
differentiation
Laplace transforms
Efros theorem
title On the Laplace Transforms of Derivatives of Special Functions with Respect to Parameters
title_full On the Laplace Transforms of Derivatives of Special Functions with Respect to Parameters
title_fullStr On the Laplace Transforms of Derivatives of Special Functions with Respect to Parameters
title_full_unstemmed On the Laplace Transforms of Derivatives of Special Functions with Respect to Parameters
title_short On the Laplace Transforms of Derivatives of Special Functions with Respect to Parameters
title_sort on the laplace transforms of derivatives of special functions with respect to parameters
topic Mittag–Leffler function
Le Roy-type function
differentiation
Laplace transforms
Efros theorem
url https://www.mdpi.com/2227-7390/13/12/1980
work_keys_str_mv AT sergeirogosin onthelaplacetransformsofderivativesofspecialfunctionswithrespecttoparameters
AT filippogiraldi onthelaplacetransformsofderivativesofspecialfunctionswithrespecttoparameters
AT francescomainardi onthelaplacetransformsofderivativesofspecialfunctionswithrespecttoparameters