Changhee Numbers Research Articles

Applications on the Apostol-Daehee numbers and polynomials associated with special numbers, polynomials, and p-adic integrals

In this paper, by using p-adic Volkenborn integral, and generating functions, we give some properties of the Bernstein basis functions, the Apostol-Daehee numbers and polynomials, Apostol-Bernoulli polynomials, some special numbers including the Stirling numbers, the Euler numbers, the Daehee numbers, and the Changhee numbers. By using an integral equation and functional equations of the generating functions and their partial differential equations (PDEs), we give a recurrence relation for the Apostol-Daehee polynomials. We also give some identities, relations, and integral representations for these numbers and polynomials. By using these relations, we compute these numbers and polynomials. We make further remarks and observations for special polynomials and numbers, which are used to study elementary word problems in engineering and in medicine.

On Appell-type Changhee polynomials and numbers

In this paper, we consider the Appell-type Changhee polynomials and derive some properties of these polynomials. Furthermore, we investigate certain identities for these polynomials.

Some identities for generalized Changhee numbers and polynomials

Some identities for generalized Changhee numbers and polynomials

THE n-TH TWISTED CHANGHEE POLYNOMIALS AND NUMBERS

The Changhee polynomials and numbers are introduced in (6). Some interesting identities and properties of those polynomials are derived from umbral calculus (see (6)). In this paper, we consider Witt- type formula for the n-th twisted 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 special polynomials.

On a q-analog of some numbers and polynomials

In this paper, we introduce new q-analogs of the Changhee numbers and polynomials of the first kind and of the second kind. We also derive some new interesting identities related to the Stirling numbers of the first kind and of the second kind, the Euler polynomials of higher order and the q-analogs of Euler polynomials by applying the p-adic integrals method and some summation transform techniques. It turns out that some well-known results are derived as special cases.

A note on weighted Changhee polynomials and numbers

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.

A note on twisted Changhee polynomials and numbers with weight

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 twisted Changhee numbers and polynomials with weight 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. Mathematics Subject Classification: 11S80, 11B68, 05A30

A note on q-Changhee polynomials and numbers

Recently, Changhee polynomials and numbers are introduced in (6). Some interesting identities and properties of those polynomials are derived from umbral calculus(see (6)). In this paper, we consider Witt-type formula for the 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 special polynomials.

Higher-order Changhee numbers and polynomials

In this paper, we consider the higher-order Changhee numbers and polynomials which are derived from the fermionic p-adic integral on Zp and give some relations between higher-order Changhee polynomials and special polynomials.