Some Relations of Two Type 2 Polynomials and Discrete Harmonic Numbers and Polynomials

Abstract

Harmonic numbers appear, for example, in many expressions involving Riemann zeta functions. Here, among other things, we introduce and study discrete versions of those numbers, namely the discrete harmonic numbers. The aim of this paper is twofold. The first is to find several relations between the Type 2 higher-order degenerate Euler polynomials and the Type 2 high-order Changhee polynomials in connection with the degenerate Stirling numbers of both kinds and Jindalrae–Stirling numbers of both kinds. The second is to define the discrete harmonic numbers and some related polynomials and numbers, and to derive their explicit expressions and an identity.

Keywords

• degenerate Stirling number of the first kind
• degenerate Stirling number of the second kind
• Jindalrae–Stirling number of the first kind
• Jindalrae–Stirling number of the second kind
• Type 2 degenerate Euler polunomial
• Type 2 Changhee polynomial