Laguerre-Type Bernoulli and Euler Numbers and Related Fractional Polynomials

Paolo Emilio Ricci; Rekha Srivastava; Diego Caratelli

doi:10.3390/math12030381

Laguerre-Type Bernoulli and Euler Numbers and Related Fractional Polynomials

Paolo Emilio Ricci (Corresponding author), Rekha Srivastava (Corresponding author), Diego Caratelli (Corresponding author)

Electromagnetics

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4 Citations (Scopus)

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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.

Original language	English
Article number	381
Number of pages	16
Journal	Mathematics
Volume	12
Issue number	3
DOIs	https://doi.org/10.3390/math12030381
Publication status	Published - Feb 2024

Bibliographical note

Publisher Copyright:
© 2024 by the authors.

Keywords

Bernoulli numbers and polynomials
Euler numbers and polynomials
generalized Laplace transform
generating functions
Laguerre-type exponential functions

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N2 - 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.

AB - 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.

KW - Bernoulli numbers and polynomials

KW - Euler numbers and polynomials

KW - generalized Laplace transform

KW - generating functions

KW - Laguerre-type exponential functions

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ER -

Laguerre-Type Bernoulli and Euler Numbers and Related Fractional Polynomials

Abstract

Bibliographical note

Keywords

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