Glasnik Matematicki, Vol. 48, No. 2 (2013), 249-263.

THE ARAKAWA-KANEKO ZETA FUNCTION AND POLY-BERNOULLI POLYNOMIALS

Yoshinori Hamahata

Institute for Teaching and Learning, Ritsumeikan University, 1-1-1 Nojihigashi, Kusatsu, Shiga 525-8577, Japan
e-mail: hamahata@fc.ritsumei.ac.jp


Abstract.   The purpose of this paper is to introduce a generalization of the Arakawa-Kaneko zeta function and investigate their special values at negative integers. The special values are written as the sums of products of Bernoulli and poly-Bernoulli polynomials. We establish the basic properties for this zeta function and their special values.

2010 Mathematics Subject Classification.   11B68, 11M32.

Key words and phrases.   Arakawa-Kaneko zeta function, Bernoulli numbers and polynomials, poly-Bernoulli numbers and polynomials.


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DOI: 10.3336/gm.48.2.03


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