Some Explicit Formulas of Hurwitz Lerch type Poly-Cauchy Polynomials and Poly-Bernoulli Polynomials

In this paper, the Hurwitz-Lerch poly-Cauchy and poly-Bernoulli polynomials are defined using polylogarithm factorial function. Some properties of these types of polynomials were also established. Specifically, two different forms of explicit formula of Hurwitz-Lerch type polyCauchy polynomials were obtained using Stirling numbers of the first and second kind and an explicit formula of Hurwitz-Lerch type poly-Bernoulli polynomials was established using the Stirling numbers of the first kind.