Abstract
In this paper, we propose a parametric kind of poly-Bernoulli polynomials by defining the two specific generating functions. We also investigate some analytical properties (for example, summation formulae, differential formulae and relations with other well-known polynomials and numbers) for our introduced polynomials in a systematic way. Furthermore, we derive two interesting connections of our parametric poly-Bernoulli polynomials with the familiar Voigt functions.