Vol. 208, No. 1, 2003
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Sums of products of generalized Bernoulli polynomials

Kwang-Wu Chen

Abstract

In this paper, we investigate the zeta function

Z(P,χ,a,s) = ∑ n1=1∞⋯∑ nr=1∞χ1(n1)⋯χr(nr)
• P(n1 + a1,…,nr + ar)−s,
where ai ≥ 0, χi is a Dirichlet character with conductor Ni, and P is a polynomial satisfying certain conditions. Its special values at nonpositive integers are closely related to generalized Bernoulli polynomials. Using this fact we can easily get sums of products of Euler polynomials and generalized Bernoulli polynomials.
Authors
Kwang-Wu Chen
Department of International Trade
Ching-Yun Institute of Technology
Jungli City, Taoyuan 320, Taiwan
Republic of China