A note on weighted Changhee polynomials and numbers

Abstract

The Changhee polynomials and numbers are introduced by D.S. Kim et al in [5]. Some interesting identities and properties of those polynomials are derived from umbral calculus(see [5]). In this paper, we consider Witt-type formula for the weighted Changhee numbers and polynomials and derive some new interesting identities and properties of those polynomials and numbers from the Witt-type formula which are related to the weighted Euler polynomials.

Some Identities Involving the Higher-Order Changhee Numbers and Polynomials

“…In [1], D.S.Kim and T.Kim give various identities of the higher-order Changhee numbers and polynomials which are derived from umbral calculas. In [3], J.Kwon consider Witt-type formula for the weighted Changhee numbers and polynomials. In [4], D.S.Kim and T.Kim also introduced the non-linear Changhee differential equations and these differential equations turned out to be very useful for special polynomials and mathematical physics and so on.…”

Differential equations for Changhee polynomials and their applications

“…Recently, several authors have studied Changhee polynomials and numbers (see [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19]). In this paper, we consider differential equations derived from the generating function of Changhee polynomials and give some new and explicit formulae for the Changhee polynomials by using our results on differential equations.…”

Differential equations for Changhee polynomials and their applications

“…Recently, several authors have studied Changhee polynomials and numbers (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]). In this paper, we consider differential equations derived from the generating function of Changhee polynomials and give some new and explicit formulae for the Changhee polynomials by using our results on differential equations.…”