Laguerre-Type Bernoulli and Euler Numbers and Related Fractional Polynomials

被引：2

作者：

Ricci, Paolo Emilio ^{[1
]}

Srivastava, Rekha ^{[2
]}

Caratelli, Diego ^{[3
]}

机构：

[1] Int Telemat Univ UniNettuno, Math Sect, Corso Vittorio Emanuele 2 39, I-00186 Rome, Italy

[2] Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3R4, Canada

[3] Eindhoven Univ Technol, Dept Elect Engn, NL-5600 MB Eindhoven, Netherlands

来源：

MATHEMATICS | 2024年 / 12卷 / 03期

关键词：

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

D O I：

10.3390/math12030381

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 (c) (latest v. 14.0).

引用

页数：16

共 19 条

[1] Commutative and associative properties of the Caputo fractional derivative and its generalizing convolution operator
Beghin, Luisa
Caputo, Michele
[J]. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2020, 89
[2] Explicit Formulas Associated with Some Families of Generalized Bernoulli and Euler Polynomials
Boutiche, M. A.
Rahmani, M.
Srivastava, H. M.
[J]. MEDITERRANEAN JOURNAL OF MATHEMATICS, 2017, 14 (02)
[3] Fractional Bernoulli and Euler Numbers and Related Fractional Polynomials-A Symmetry in Number Theory
Caratelli, Diego
Natalini, Pierpaolo
Ricci, Paolo Emilio
[J]. SYMMETRY-BASEL, 2023, 15 (10):
[4] Comtet L., 1974, Advanced Combinatorics
[5] Dattoli G., 2003, GEORGIAN MATH J, V10, P481, DOI DOI 10.1515/GMJ.2003.481
[6] Delerue P., 1953, ANN SOC SCI BRUX, V3, P229
[7] Dimovski I., 1966, C. R. Acad. Bulgare Sci., V19, P1111
[8] Gorenflo R., 2014, Mittag-Leffler functions, related topics and applications, DOI DOI 10.1007/978-3-662-43930-2
[9] Higher-Order Convolutions for Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi Polynomials
He, Yuan
Araci, Serkan
Srivastava, Hari M.
Abdel-Aty, Mahmoud
[J]. MATHEMATICS, 2018, 6 (12):
[10] Kilbas A., 2006, Theory and Applications of Fractional Differential Equations

← 1 2 →