Some Explicit Formula of Hurwitz Lerch type Poly-Cauchy Polynomials and Poly-Bernoulli Polynomials
DOI:
https://doi.org/10.29020/nybg.ejpam.v16i3.4825Keywords:
polylogarithm factorial functions, poly-Cauchy numbers of the first and second kind, poly-Bernoulli numbers, Hurwitz–Lerch factorial zeta function, generating functionAbstract
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.
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