On Certain Recurrence Relations for Generalized Poly-Cauchy Numbers and Polynomials

TL;DR

This paper introduces recurrence relations for generalized poly-Cauchy numbers and polynomials, along with related generalized m-poly-Bernoulli numbers, expanding the theoretical framework of these special number sequences.

Contribution

It defines generalized m-poly-Cauchy and m-poly-Bernoulli numbers and polynomials, establishing new recurrence relations and theoretical connections among these generalized sequences.

Findings

Derived recurrence relations for generalized poly-Cauchy numbers

Established links between generalized m-poly-Cauchy and m-poly-Bernoulli numbers

Expanded the theoretical understanding of these generalized special numbers

Abstract

The main objective of this paper is to present recurrence relations for the generalized poly-Cauchy numbers and polynomials. This is accomplished by introducing the concept of generalized m-poly-Cauchy numbers and polynomials. Additionally, the paper delves into the discussion of the corresponding generalized m-poly-Bernoulli numbers and polynomials that are associated with the aforementioned generalized m-poly-Cauchy numbers and polynomials.