Bulletin of the
Korean Mathematical Society BKMS

L. Carlitz introduced higher order degenerate Euler polynomials in \cite{A4,A5} and studied a degenerate Staudt-Clausen theorem in \cite{A4}. D. S. Kim and T. Kim gave some formulas and identities of degenerate Euler polynomials which are derived from the fermionic $p$-adic integrals on $\mathbb{Z}_p$ (\mbox{see~~\cite{A11}}). In this paper, we introduce higher order degenerate Genocchi polynomials. And we give some formulas and identities of degenerate Genocchi polynomials which are derived from the fermionic $p$-adic integrals on $\mathbb{Z}_p$.

Keywords: degenerate Genocchi polynomial, femionic $p$-adic integral

MSC numbers: Primary 11B68, 11B75, 11B83, 33E30, 33F99