Explicit Formulae of Cauchy Polynomials with a $q$ Parameter in Terms of $r$-Whitney Numbers

TL;DR

This paper derives explicit formulas for Cauchy polynomials with a q parameter using r-Whitney numbers, expanding understanding of their properties and identities.

Contribution

It introduces explicit formulae connecting Cauchy polynomials with r-Whitney numbers, providing new combinatorial identities and properties.

Findings

Explicit formulae for Cauchy polynomials with q parameter

New combinatorial identities involving r-Whitney numbers

Enhanced understanding of arithmetical properties of these polynomials

Abstract

The Cauchy polynomials with a $q$ parameter were recently defined, and several arithmetical properties were studied. In this paper, we establish explicit formulae for computing the Cauchy polynomials with a $q$ parameter in terms of $r$-Whitney numbers of the first kind. We also obtain several properties and combinatorial identities.