Sums of products of q-Bernoulli numbers

被引：34
|
作者：
Kim, T
机构：
[1] Jangjun Res Inst Math Sci, Kyungshang Nam Do 678800, South Korea
[2] Simon Fraser Univ, Dept Math, Burnaby, BC V5A 1S6, Canada
来源：
ARCHIV DER MATHEMATIK | 2001年 / 76卷 / 03期
关键词：
D O I：
10.1007/s000130050559
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We define Carlitz's q-Bernoulli number of higher order using an integral by the q-analogue mu (q) [4] of the ordinary p-adic invariant measure. Using q-Bernoulli number of higher order, we give the formula for sums of products of Carlitz's q-Bernoulli numbers of the form [GRAPHICS] x beta (k1+i1)(alpha (1),q)beta (k2+i2) (alpha (2), q) . . . beta (kl-1+l-1) (alpha (l-1), q)beta (il)(alpha (l),q)(q - 1)(k1 + . . . + kl-1), where beta (m)(alpha, q) is the Carlitz's q-Bernoulli polynomial.
引用
收藏
页码：190 / 195
页数：6
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