A Note on a Closed Formula for Poly-Bernoulli Numbers
A Note on a Closed Formula for Poly-Bernoulli Numbers
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关于聚伯努利数闭式公式的注解
DOI：
10.1080/00029890.2002.11919909
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发表时间：
2002
期刊：
影响因子：
--
通讯作者：
Roberto Sánchez
中科院分区：
文献类型：
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作者：
Roberto Sánchez
1.导论.本文给出了poly-Bernoulli数的一个性质的初等证明，即T. Arakawa和M. Kaneko和R. Sánchez-Peregrino [4].文[2]定义并研究了多Bernoulli数，它推广了经典Bernoulli数.对于每一个整数k，我们定义指数k的多伯努利数为有理数序列Bk n（n= 0，1，2，.）形式恒等式1 z
1. INTRODUCTION. In the present note we give an elementary proof of a property of the poly-Bernoulli numbers; namely, the closed form expression for negatively indexed poly-Bernoulli numbers established by T. Arakawa and M. Kaneko [1] and R. Sánchez-Peregrino [4]. In [2], the poly-Bernoulli numbers, which generalize the classical Bernoulli numbers, were defined and studied. For each integer k we define the poly-Bernoulli numbers of index k to be the sequence of rational numbers Bk n (n= 0, 1, 2,...) for which the formal identity 1 z