A New Formula for the Bernoulli Polynomials

被引：86
|
作者：
Mezo, Istvan [1 ]
机构：
[1] Univ Debrecen, Fac Informat, Dept Appl Math & Probabil Theory, H-4010 Debrecen, Hungary
来源：
RESULTS IN MATHEMATICS | 2010年 / 58卷 / 3-4期
关键词：
Stirling numbers; r-Stirling numbers; Whitney numbers; Bernoulli polynomials; Harmonic numbers; Stirling-type pairs; Hyperharmonic numbers; Harmonic polynomials; STIRLING NUMBERS;
D O I：
10.1007/s00025-010-0039-z
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this note we show that a seemingly new class of Stirling-type pairs can be applied to produce a new representation of the Bernoulli polynomials at positive rational arguments. A class of generalized harmonic numbers is also investigated, and we point out that these give a new relation for the so-called harmonic polynomials.
引用
收藏
页码：329 / 335
页数：7
相关论文
共 50 条
  • [41] Algorithms for Bernoulli and Related Polynomials
    Dil, Ayhan
    Kurt, Veli
    Cenkci, Mehmet
    JOURNAL OF INTEGER SEQUENCES, 2007, 10 (05)
  • [42] MONOTONICITY OF RATIOS OF BERNOULLI POLYNOMIALS
    Pinelis, Iosif
    MATHEMATICAL INEQUALITIES & APPLICATIONS, 2024, 27 (04): : 949 - 953
  • [43] On multiple zeros of Bernoulli polynomials
    Dilcher, Karl
    ACTA ARITHMETICA, 2008, 134 (02) : 149 - 155
  • [44] A note on the Bernoulli and Euler polynomials
    Cheon, GS
    APPLIED MATHEMATICS LETTERS, 2003, 16 (03) : 365 - 368
  • [45] Integrals of products of Bernoulli polynomials
    Agoh, Takashi
    Dilcher, Karl
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 381 (01) : 10 - 16
  • [46] Triple convolution identities on Bernoulli polynomials and Euler polynomials
    Wang, Weiping
    Liu, Hongmei
    Jia, Cangzhi
    UTILITAS MATHEMATICA, 2016, 101 : 369 - 395
  • [47] Poly-Bernoulli numbers and polynomials with a q parameter
    Cenkci, Mehmet
    Komatsu, Takao
    JOURNAL OF NUMBER THEORY, 2015, 152 : 38 - 54
  • [48] Two closed forms for the Apostol-Bernoulli polynomials
    Hu, Su
    Kim, Min-Soo
    RAMANUJAN JOURNAL, 2018, 46 (01) : 103 - 117
  • [49] Some sum relations involving Bernoulli and Euler polynomials
    He, Yuan
    Zhang, Wenpeng
    INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2011, 22 (03) : 207 - 215
  • [50] Probabilistic Multiple Poly Bernoulli Polynomials of the Second Kind
    Lee, Si Hyeon
    Chen, Li
    EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 2025, 18 (01):
12345