Poly-Cauchy numbers and polynomials of the second kind

TL;DR

This paper explores the properties and identities of poly-Cauchy polynomials of the second kind, linking them to generalized Bernoulli polynomials and deriving new identities using umbral calculus.

Contribution

It provides new identities for poly-Cauchy polynomials of the second kind, highlighting their relation to generalized Bernoulli polynomials and applying umbral calculus techniques.

Findings

Poly-Cauchy polynomials of the second kind are special generalized Bernoulli polynomials.

Various identities of these polynomials are derived using umbral calculus.

The work extends understanding of poly-Cauchy polynomials and their algebraic properties.

Abstract

In this paper, we consider the poly-cauchy polynomials and numbers of the second kind which were studied by Komatsu in [10]. We note that the poly-Cauchy polynomials of the second kind are the special generalized Bernoulli polynomials of the second kind. The purpose of this paper is to give various identities of the poly-Cauchy polynomials of the second kind which are derived from umbral calculus.