Multiparameter poly-Cauchy and poly-Bernoulli numbers and polynomials

TL;DR

This paper introduces new multiparameter generalizations of poly-Cauchy and poly-Bernoulli numbers and polynomials, deriving identities and relations that extend existing mathematical frameworks.

Contribution

It presents novel multiparameter generalizations of poly-Cauchy and poly-Bernoulli numbers and polynomials, along with new identities and relations involving Stirling numbers.

Findings

Derived identities involving the new numbers and polynomials

Established relations between multiparameter poly-Cauchy and poly-Bernoulli numbers

Extended existing mathematical relations to more general cases

Abstract

Recently, Komastu introduced the concept of poly-Cauchy numbers and polynomials which generalize Cauchy numbers and polynomials. In this paper, we introduce new generaliza- tion of poly-Cauchy and poly-Bernoulli numbers and polynomials. Also, we introduce new generalizations of Cauchy numbers and polynomials. Moreover, we derive some identities involving the new numbers and polynomials and some types of Stirling numbers. These gives generalization of some relations poly-Cauchy and poly-Bernoulli numbers and poly- nomials. Furthermore, we obtain some relations between the multiparameter poly-Cauchy numbers and polynomials and new multiparameter poly-Bernoulli numbers and polyno- mials.