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Laguerre-Type Bernoulli and Euler Numbers and Related Fractional Polynomials

Author

Listed:
  • Paolo Emilio Ricci

    (Mathematics Section, International Telematic University UniNettuno, Corso Vittorio Emanuele II 39, 00186 Rome, Italy
    These authors contributed equally to this work.)

  • Rekha Srivastava

    (Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
    These authors contributed equally to this work.)

  • Diego Caratelli

    (Department of Electrical Engineering, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands
    These authors contributed equally to this work.)

Abstract

We extended the classical Bernoulli and Euler numbers and polynomials to introduce the Laguerre-type Bernoulli and Euler numbers and related fractional polynomials. The case of fractional Bernoulli and Euler polynomials and numbers has already been considered in a previous paper of which this article is a further generalization. Furthermore, we exploited the Laguerre-type fractional exponentials to define a generalized form of the classical Laplace transform. We show some examples of these generalized mathematical entities, which were derived using the computer algebra system Mathematica© (latest v. 14.0).

Suggested Citation

  • Paolo Emilio Ricci & Rekha Srivastava & Diego Caratelli, 2024. "Laguerre-Type Bernoulli and Euler Numbers and Related Fractional Polynomials," Mathematics, MDPI, vol. 12(3), pages 1-16, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:3:p:381-:d:1325791
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    References listed on IDEAS

    as
    1. Yuan He & Serkan Araci & Hari M. Srivastava & Mahmoud Abdel-Aty, 2018. "Higher-Order Convolutions for Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi Polynomials," Mathematics, MDPI, vol. 6(12), pages 1-14, December.
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