Recursion Formulas for Bernoulli Numbers

被引：0
|
作者：
Kim, Aeran [1 ]
机构：
[1] Private Math Acad, 1-406,23,Maebong 5 Gil, Chonju 54921, Chonbuk, South Korea
来源：
THAI JOURNAL OF MATHEMATICS | 2022年 / 20卷 / 01期
关键词：
Bernoulli numbers; Lucas sequence; recursion theory;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we establish simple recursion formulas for Bernoulli numbers, for instance, Sigma(n)(k=1) (4n + 2 4k) (-1)(k)2(2k-1) B-4k = n and Sigma(n)(k=0) (4n + 4 4k + 2) (-1)(k)2(2k) B4k+2 = n + 1 in Theorem 1.1. Furthermore applying a Lucas sequence V-n, we obtain Sigma(n)(k=1) (8n + 4 8k) (-1)(k)2(2k-1) B8kV4n-4k+2 = nV(4n+2) and Sigma(n)(k=0) (8n + 8 8k + 4) (-1)(k)2(2k) B8k+4V4n-4k+2 = -(n + 1)V4n+3 in Theorem 1.2.
引用
收藏
页码：55 / 67
页数：13
相关论文
共 50 条
  • [41] Shortened recurrence relations for Bernoulli numbers
    Agoh, Takashi
    Dilcher, Karl
    DISCRETE MATHEMATICS, 2009, 309 (04) : 887 - 898
  • [42] BERNOULLI NUMBERS AND CONGRUENCES FOR HARMONIC SUMS
    Xia, Binzhou
    Cai, Tianxin
    INTERNATIONAL JOURNAL OF NUMBER THEORY, 2010, 6 (04) : 849 - 855
  • [43] SOME ARITHMETIC PROPERTIES OF BERNOULLI NUMBERS
    Robbins, Neville
    JP JOURNAL OF ALGEBRA NUMBER THEORY AND APPLICATIONS, 2005, 5 (01): : 201 - 204
  • [44] On Generalized Fibonacci Polynomials and Bernoulli Numbers
    Zhang, Tianping
    Ma, Yuankui
    JOURNAL OF INTEGER SEQUENCES, 2005, 8 (05)
  • [45] Bernoulli numbers and multiple zeta values
    Nakamura, T
    PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 2005, 81 (02) : 21 - 22
  • [46] Scale Invariant Scattering and Bernoulli Numbers
    Curtright, Thomas L.
    SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 2024, 20
  • [47] Generalized Bernoulli Polynomials and Numbers, Revisited
    Neven Elezović
    Mediterranean Journal of Mathematics, 2016, 13 : 141 - 151
  • [48] The p-adic Valuation of Eulerian Numbers: Trees and Bernoulli Numbers
    Castro, Francis N.
    Gonzalez, Oscar E.
    Medina, Luis A.
    EXPERIMENTAL MATHEMATICS, 2015, 24 (02) : 183 - 195
  • [49] Incomplete poly-Bernoulli numbers associated with incomplete Stirling numbers
    Komatsu, Takao
    Liptai, Kalman
    Mezo, Istvan
    PUBLICATIONES MATHEMATICAE-DEBRECEN, 2016, 88 (3-4): : 357 - 368
  • [50] Arithmetic Identities Involving Bernoulli and Euler Numbers
    Chu, Wenchang
    Wang, Chenying
    RESULTS IN MATHEMATICS, 2009, 55 (1-2) : 65 - 77
12345