  In this paper, we obtain new relationships between the Cauchy polynomials,
the Bernoulli polynomials, and the generalized (or weighted) Stirling numbers
of both kinds. Furthermore, we derive some identities involving the Cauchy
polynomials, the Daehee polynomials, and the hyperharmonic polynomials. In
addition, we consider the poly-Cauchy polynomials and the weighted type
poly-Bernoulli polynomials and retrieve some of their relationships in the
light of our previous findings. Finally, we give various relationships
involving the rational values of the Cauchy polynomials and those of the
Bernoulli polynomials in terms of $r$-Whitney numbers.
