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

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.