On generalized degenerate Euler-Genocchi polynomials

Abstract

We introduce the generalized degenerate Euler-Genocchi polynomials as a degenerate version of the Euler-Genocchi polynomials. In addition, we introduce their higher-order version, namely the generalized degenerate Euler-Genocchi polynomials of order {\alpha}, as a degenerate version of the generalized Euler-Genocchi polynomials of order {\alpha}. The aim of this paper is to study certain properties and identities involving those polynomials, the generalized falling factorials, the degenerate Euler polynomials of order {\alpha}, the degenerate Stirling numbers of the second kind, and the alternating degenerate power sum of integers.