Shifted poly-Cauchy numbers

Abstract

Recently, the first author introduced the concept of poly-Cauchy numbers as a generalization of the classical Cauchy numbers and an analogue of poly-Bernoulli numbers. This concept has been generalized in various ways, including poly-Cauchy numbers with a q parameter. In this paper, we give a different kind of generalization called shifted poly-Cauchy numbers and investigate several arithmetical properties. Such numbers can be expressed in terms of original poly-Cauchy numbers. This concept is a kind of analogous ideas to that of Hurwitz zeta-functions compared to Riemann zeta-functions.