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

Author

Listed:
  • 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
    School of Chemistry and Physics, University of KwaZulu-Natal, Westville Campus, Durban 4000, South Africa)

  • Francesco Mainardi

    (Department of Physics & Astronomy, University of Bologna, and INFN, Via Irnerio 46, 40126 Bologna, Italy)

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.

Suggested Citation

  • Sergei Rogosin & Filippo Giraldi & Francesco Mainardi, 2025. "On the Laplace Transforms of Derivatives of Special Functions with Respect to Parameters," Mathematics, MDPI, vol. 13(12), pages 1-14, June.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:12:p:1980-:d:1679863
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