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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| Format: | Article |
| Language: | English |
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MDPI AG
2025-06-01
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| Series: | Mathematics |
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| 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. |
| format | Article |
| id | doaj-art-f2e2491277344e4eae62c56c85418af2 |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| 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 |