A Note on Multi-Euler-Genocchi and Degenerate Multi-Euler-Genocchi Polynomials

Abstract

Recently, the generalized Euler-Genocchi and generalized degenerate Euler-Genocchi polynomials are introduced. The aim of this note is to study the multi-Euler-Genocchi and degenerate multi-Euler-Genocchi polynomials which are defined by means of the multiple logarithm and generalize, respectively, the generalized Euler-Genocchi and generalized degenerate Euler-Genocchi polynomials. Especially, we express the former by the generalized Euler-Genocchi polynomials, the multi-Stirling numbers of the first kind and Stirling numbers of the second kind, and the latter by the generalized degenerate Euler-Genocchi polynomials, the multi-Stirling numbers of the first kind and Stirling numbers of the second kind.