The higher-order type 2 Daehee polynomials associated with p-adic integral on ℤp

Abstract

In this paper, the higher-order type 2 Daehee polynomials are introduced and some of their relations and properties are derived. Then, some p-adic integral representations of not only higher-order type 2 Daehee polynomials and numbers but also type 2 Daehee polynomials and numbers are acquired. Several identities and relations related to both central factorial numbers of the second kind and Stirling numbers of the first and second kinds are investigated. Moreover, the conjugate higher-order type 2 Daehee polynomials are considered and some correlations covering the type 2 Daehee polynomials of order β and the conjugate higher-order type 2 Daehee polynomials are attained.

Keywords

• type 2 daehee polynomials
• higher-order type 2 daehee polynomials
• p-adic integral
• the central factorial numbers of the second kind
• stirling numbers of the first and second kinds