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SPECIAL VALUES OF SOME EXTENSIONS OF ZETA FUNCTION VIA BETA DISTRIBUTIONS

NORIYOSHI SAKUMA

Department of Mathematics, Aichi University of Education, Japan

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and

RYOICHI SUZUKI

Department of Mathematics, Keio University, 3-14-1 Hiyoshi Kohoku-ku, Yokohama 223-8522, Japan

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https://doi.org/10.1142/S0219025712500087Cited by:0 (Source: Crossref)

Abstract

In this paper, we show the Basel problem via the beta distributions, which include the free Poisson distribution and positive arcsine law. This is a generalization of Ref. 2 by Fujita. We also obtain special values of an extension of generalized Hurwitz–Lerch zeta function, which was introduced by Gang, Jain and Kalla.

Keywords:

AMSC: 11M06, 11M41, 60E05

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