Analysis of higher-order Peters-type combinatorial numbers and polynomials by their generating functions and p-adic integration - Kucukoglu, Irem (AIP conference proceedings, 2020)
The aim of this paper is to analyze higher-order Peters-type combinatorial numbers and polynomials by means of their generating functions and p-adic integration. By using generating functions we first obtain a combinatorial identity containing not only these numbers and polynomials, but also the Stirling numbers of the first kind, the falling factorial and binomial coefficients. Secondly, by implementation of p-adic integration into the combinatorial sum representation of higher-order Peters-type combinatorial polynomials which includes falling factorial function, we provide both bosonic and fermionic p-adic integral representations of these numbers and polynomials. 2010 Mathematics Subject Classification: 05A10, 05A15, 11B83, 11S23, 11S80, 40C10.