Convolution identities of poly-Cauchy numbers with level 2

Abstract

Poly-Cauchy numbers with level 2 are defined by inverse sine hyperbolic functions with the inverse relation from sine hyperbolic functions. In this paper, we introduce the Stirling numbers of the first kind with level 2 in order to establish some relations with poly- Cauchy numbers with level 2. Then, we show several convolution identities of poly-Cauchy numbers with level 2. In particular, that of three poly-Cauchy numbers with level 2 can be expressed as a simple form.