Some identities related to degenerate Bernoulli and degenerate Euler polynomials

被引:1
作者
Kim, Taekyun [1 ]
Kim, Dae San [2 ]
Kim, Wonjoo [3 ]
Kwon, Jongkyum [4 ]
机构
[1] Kwangwoon Univ, Math, Seoul, South Korea
[2] Sogang Univ, Math, Seoul, South Korea
[3] Kyung Hee Univ, Math, Seoul, South Korea
[4] Gyeongsang Natl Univ, Math Educ, Jinju, South Korea
关键词
degenerate Bernoulli polynomials; degenerate Euler polynomials; higher-order degenerate Bernoulli polynomials; higher-order degenerate Euler polynomials; NUMBERS;
D O I
10.1080/13873954.2024.2425155
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
The aim of this paper is to study degenerate Bernoulli and degenerate Euler polynomials and numbers and their higher-order analogues. We express the degenerate Euler polynomials in terms of the degenerate Bernoulli polynomials and vice versa. We prove the distribution formulas for degenerate Bernoulli and degenerate Euler polynomials. We obtain some identities among the higher-order degenerate Bernoulli and higher-order degenerate Euler polynomials. We express the higher-order degenerate Bernoulli polynomials in $x + y$x+y as a linear combination of the degenerate Euler polynomials in $y$y. We get certain identities involving the degenerate $r$r-Stirling numbers of the second and the binomial coefficients.
引用
收藏
页码:882 / 897
页数:16
相关论文
共 36 条
  • [1] Abramowitz M., 1964, HDB MATH FUNCTIONS F
  • [2] Aydin MS., 2022, Proc Jangjeon Math Soc, V25, P195
  • [3] Carlitz L., 1956, Arch. Math., V7, P28
  • [4] Carlitz L., 1979, UTILITAS MATHEMATICA, V15, P51, DOI 10.12691/tjant-3-4-3
  • [5] Probabilistic degenerate central Bell polynomials
    Chen, Li
    Kim, Taekyun
    Kim, Dae San
    Lee, Hyunseok
    Lee, Si-Hyeon
    [J]. MATHEMATICAL AND COMPUTER MODELLING OF DYNAMICAL SYSTEMS, 2024, 30 (01) : 523 - 542
  • [6] Probabilistic type 2 Bernoulli and Euler polynomials
    Chen, Li
    Dolgy, Dmitry, V
    Kim, Taekyun
    Kim, Dae San
    [J]. AIMS MATHEMATICS, 2024, 9 (06): : 14312 - 14324
  • [7] Comtet L., 1974, ADV COMBINATORICS AR
  • [8] Dolgy DV., 2023, Adv Stud Contemp Math (Kyungshang), V33, P111
  • [9] Erdlyi A., 1981, Higher transcendental functions. Vol. I. Based on notes left by Harry Bateman. With a preface by Mina Rees. With a foreword by E. C. Watson
  • [10] Gun D., 2020, Adv Stud Contemp Math (Kyungshang), V30, P503