Probabilistic type 2 Bernoulli and Euler polynomials-Reference-Cited by-同舟云学术

Probabilistic type 2 Bernoulli and Euler polynomials

Published:2024 Issue:6 Volume:9 Page:14312-14324
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Chen Li¹,Dolgy Dmitry V.²,Kim Taekyun³⁴,Kim Dae San⁵

Affiliation:

1. School of Mathematics, Xi'an University of Finance and Economics, Xi'an, China

2. Kwangwoon Global Education Center, Kwangwoon University, Seoul 139-701, Republic of Korea

3. Department of Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea

4. School of Science, Xi'an Technological University, Xi'an 710021, Shaanxi, China

5. Department of Mathematics, Sogang University, Seoul 121-742, Republic of Korea

Abstract

<abstract><p>Assume that the moment-generating function of the random variable $ Y $ exists in a neighborhood of the origin. The aim of this paper is to investigate the probabilistic type 2 Bernoulli polynomials associated with $ Y $ and the probabilistic type 2 Euler polynomials associated with $ Y $, along with the probabilistic type 2 cosine-Bernoulli polynomials associated with $ Y $, the probabilistic type 2 sine-Bernoulli polynomials associated with $ Y $, the probabilistic type 2 cosine-Euler polynomials associated with $ Y $, and the probabilistic type 2 sine-Euler polynomials associated with $ Y $. We deal with their properties, related identities and explicit expressions.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Reference20 articles.

1. M. Abbas, S. Bouroubi, On new identities for Bell's polynomials, Discrete Math., 293 (2005), 5–10. https://doi.org/10.1016/j.disc.2004.08.023

2. M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, New York: Dover, 1992.

3. J. A. Adell, Probabilistic Stirling numbers of the second kind and applications, J. Theor. Probab., 35 (2022), 636–652. https://doi.org/10.1007/s10959-020-01050-9

4. A. Z. Broder, The $r$-Stirling numbers, Discrete Math., 49 (1984), 241–259. https://doi.org/10.1016/0012-365X(84)90161-4

5. L. Carlitz, Some remarks on the Bell numbers, Fibonacci Quart., 18 (1980), 66–73.

Cited by 3 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Exploring probabilistic Bernstein polynomials: identities and applications;Applied Mathematics in Science and Engineering;2024-09-05

2. Probabilistic Type 2 poly-Bernoulli Polynomials;European Journal of Pure and Applied Mathematics;2024-07-31

3. A probabilistic proof of some integral formulas involving incomplete gamma functions;Communications in Statistics - Theory and Methods;2024-06-30