A new explicit formula for the Bernoulli numbers in terms of the Stirling numbers of the second kind

被引：0
|
作者：
Jha, Sumit Kumar [1 ]
机构：
[1] Int Inst Informat Technol, Hyderabad 500032, India
来源：
NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS | 2020年 / 26卷 / 02期
关键词：
Bernoulli numbers; Stirling numbers of the second kind; Riemann zeta function; Polylogarithm function;
D O I：
10.7546/nntdm.2020.26.2.148-151
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let B-r denote the Bernoulli numbers, and S (r , k) denote the Stirling numbers of the second kind. We prove the following explicit formula Br+1 = Sigma(r)(k=0) (-1)(k-1)k! S(r,k)/(k + 1) (k +2). To the best of our knowledge, the formula is new.
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页码：148 / 151
页数：4
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