A note on degenerate Genocchi and poly-Genocchi numbers and polynomials

Abstract

Abstract Recently, Dolgy–Jang introduced the poly-Genocchi polynomials and numbers arising from the modified polyexponential function. In this paper, we study the degenerate poly-Genocchi polynomials and numbers constructed from the modified degenerate polyexponential function. We derive explicit expressions for those polynomials and numbers. Also, we obtain identities involving those polynomials and numbers and some other special numbers and polynomials. In addition, we investigate the higher-order degenerate Genocchi polynomials and find identities involving those polynomials and the higher-order Changhee polynomials.

Keywords

• Degenerate poly-Genocchi polynomials and numbers
• Modified degenerate polyexponential functions
• Higher-order degenerate Genocchi polynomials and numbers
• Higher-order Changhee polynomials and numbers