Some Identities of Ordinary and Degenerate Bernoulli Numbers and Polynomials

被引：1

作者：

Dolgy, Dmitry, V ^{[1
]}

Kim, Dae San ^{[2
]}

Kwon, Jongkyum ^{[3
]}

Kim, Taekyun ^{[4
]}

机构：

[1] Kwangwoon Univ, Hanrimwon, Seoul 139701, South Korea

[2] Sogang Univ, Dept Math, Seoul 121742, South Korea

[3] Gyeongsang Natl Univ, Dept Math Educ & ERI, Jinju 52828, Gyeongsangnamdo, South Korea

[4] Kwangwoon Univ, Dept Math, Seoul 139701, South Korea

来源：

SYMMETRY-BASEL | 2019年 / 11卷 / 07期

基金：

新加坡国家研究基金会;

关键词：

Bernoulli polynomials; degenerate Bernoulli polynomials; random variables; p-adic invariant integral on Z(p); integer power sums polynomials; Stirling polynomials of the second kind; degenerate Stirling polynomials of the second kind;

D O I：

10.3390/sym11070847

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

In this paper, we investigate some identities on Bernoulli numbers and polynomials and those on degenerate Bernoulli numbers and polynomials arising from certain p-adic invariant integrals on Z(p). In particular, we derive various expressions for the polynomials associated with integer power sums, called integer power sum polynomials and also for their degenerate versions. Further, we compute the expectations of an infinite family of random variables which involve the degenerate Stirling polynomials of the second and some value of higher-order Bernoulli polynomials.

引用

页数：13

共 19 条

[1] Extended q-Dedekind-type Daehee-Changhee sums associated with extended q-Euler polynomials
Araci, Serkan
Ozer, Ozen
[J]. ADVANCES IN DIFFERENCE EQUATIONS, 2015,
[2] Carlitz L., 1956, Arch. Math., V7, P28, DOI [10.1007/BF01900520, DOI 10.1007/BF01900520]
[3] Carlitz L., 1979, Util. Math., V15, P51
[4] New results on higher-order Daehee and Bernoulli numbers and polynomials
El-Desouky, Beih S.
Mustafa, Abdelfattah
[J]. ADVANCES IN DIFFERENCE EQUATIONS, 2016, : 1 - 21
[5] HOON RIM SEOG, 2006, [Bulletin of the KMS, 대한수학회보], V43, P611
[6] Degenerate r-Stirling Numbers and r-Bell Polynomials
Kim, T.
Yao, Y.
Kim, D. S.
Jang, G. -W.
[J]. RUSSIAN JOURNAL OF MATHEMATICAL PHYSICS, 2018, 25 (01) : 44 - 58
[7] 김택연, 2017, [Proceedings of the Jangjeon Mathematical Society, Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)], V20, P319
[8] Degenerate Laplace transform and degenerate gamma function
Kim, T.
Kim, D. S.
[J]. RUSSIAN JOURNAL OF MATHEMATICAL PHYSICS, 2017, 24 (02) : 241 - 248
[9] Kim T, 2002, RUSS J MATH PHYS, V9, P288
[10] Symmetry of power sum polynomials and multivariate fermionic p-adic invariant integral on a"currency sign p
Kim, T.
[J]. RUSSIAN JOURNAL OF MATHEMATICAL PHYSICS, 2009, 16 (01) : 93 - 96

← 1 2 →