A Generalization of Poly-Cauchy Numbers and Their Properties

Abstract EN

In Komatsu's work (2013), the concept of poly-Cauchy numbers is introduced as an analogue of that of poly-Bernoulli numbers.

Both numbers are extensions of classical Cauchy numbers and Bernoulli numbers, respectively.

There are several generalizations of poly-Cauchy numbers, including poly-Cauchy numbers with a q parameter and shifted poly-Cauchy numbers.

In this paper, we give a further generalization of poly-Cauchy numbers and investigate several arithmetical properties.

We also give the corresponding generalized poly-Bernoulli numbers so that both numbers have some relations.