Laguerre-Type Bernoulli and Euler Numbers and Related Fractional Polynomials

Paolo Emilio Ricci (), Rekha Srivastava and Diego Caratelli
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Paolo Emilio Ricci: Mathematics Section, International Telematic University UniNettuno, Corso Vittorio Emanuele II 39, 00186 Rome, Italy
Rekha Srivastava: Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
Diego Caratelli: Department of Electrical Engineering, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands

Mathematics, 2024, vol. 12, issue 3, 1-16

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).

Keywords: Bernoulli numbers and polynomials; Euler numbers and polynomials; Laguerre-type exponential functions; generating functions; generalized Laplace transform (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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