Some Explicit Formula of Hurwitz Lerch type Poly-Cauchy Polynomials and Poly-Bernoulli Polynomials (European Journal of Pure and Applied Mathematics, 2023)
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 poly-Cauchy polynomials were obtained using Stirling numbers of the first and second kinds and an explicit formula of Hurwitz-Lerch type poly-Bernoulli polynomials was established using the Stirling numbers of the first kind.
Keywords: polylogarithm factorial functions; poly-Cauchy numbers of the first and second kind; poly-Bernoulli numbers; Hurwitz–Lerch factorial zeta function; generating function