Identities for Bernoulli polynomials and Bernoulli numbers

被引：1

作者：

Alzer, Horst ^{[1
]}

Kwong, Man Kam ^{[1
]}

机构：

[1] Hong Kong Polytech Univ, Dept Appl Math, Hunghom, Hong Kong, Peoples R China

来源：

ARCHIV DER MATHEMATIK | 2014年 / 102卷 / 06期

关键词：

Bernoulli polynomials; Bernoulli numbers; identities; RECURRENCE FORMULA;

D O I：

10.1007/s00013-014-0653-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that if m and v are integers with and 0 <= v <= m and x is a real number, then [GRAPHICS] [GRAPHICS] where B (n) (x) denotes the Bernoulli polynomial of degree n. An application of (1) leads to new identities for Bernoulli numbers B (n) . Among others, we obtain [GRAPHICS] This formula extends two results obtained by Kaneko and Chen-Sun, who proved (2) for the special cases j = 1,v=0 and j = 3, v=0, respectively.

引用

页码：521 / 529

页数：9

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