Changhee Polynomials Research Articles

Notes on the Poly-Korobov polynomials and related polynomials

In recent years, many mathematicians ([2], [7], [8], [9], [15], [16], [21]) introduced and investigated for the Korobov polynomials. They gave some identities and relations for the Korobov type polynomials. In this work, we give some relations for the first kind Korobov polynomials and Korobov type Changhee polynomials. Further, wegive two relations between the poly-Changhee polynomials and the poly-Korobov polynomials. Also, we give a relation among the poly-Korobov type Changhee polynomials, the Stirling numbers of the second kind, the Euler polynomials and the Bernoulli numbers.

Identities and Computation Formulas for Combinatorial Numbers Including Negative Order Changhee Polynomials

The purpose of this paper is to construct generating functions for negative order Changhee numbers and polynomials. Using these generating functions with their functional equation, we prove computation formulas for combinatorial numbers and polynomials. These formulas include Euler numbers and polynomials of higher order, Stirling numbers, and negative order Changhee numbers and polynomials. We also give some properties of these numbers and polynomials with their generating functions. Moreover, we give relations among Changhee numbers and polynomials of negative order, combinatorial numbers and polynomials and Bernoulli numbers of the second kind. Finally, we give a partial derivative of an equation for generating functions for Changhee numbers and polynomials of negative order. Using these differential equations, we derive recurrence relations, differential and integral formulas for these numbers and polynomials. We also give p-adic integrals representations for negative order Changhee polynomials including Changhee numbers and Deahee numbers.

A note on degenerate type 2 Changhee polynomials and numbers

A note on degenerate type 2 Changhee polynomials and numbers

A Class of Sheffer Sequences of Some Complex Polynomials and Their Degenerate Types

We study some properties of Sheffer sequences for some special polynomials with complex Changhee and Daehee polynomials introducing their complex versions of the polynomials and splitting them into real and imaginary parts using trigonometric polynomial sequences. Moreover, considering their degenerate types of Sheffer sequences based on umbral composition, we present some useful expressions, properties, and examples about complex versions of the degenerate polynomials.

On applications for Mahler expansion associated with p-adic q-integrals

In this paper, we primarily consider a generalization of the fermionic [Formula: see text]-adic [Formula: see text]-integral on [Formula: see text] including the parameters [Formula: see text] and [Formula: see text] and investigate its some basic properties. By means of the foregoing integral, we introduce two generalizations of [Formula: see text]-Changhee polynomials and numbers as [Formula: see text]-Changhee polynomials and numbers with weight [Formula: see text] and [Formula: see text]-Changhee polynomials and numbers of second kind with weight [Formula: see text]. For the mentioned polynomials, we obtain new and interesting relationships and identities including symmetric relation, recurrence relations and correlations associated with the weighted [Formula: see text]-Euler polynomials, [Formula: see text]-Stirling numbers of the second kind and Stirling numbers of first and second kinds. Then, we discover multifarious relationships among the two types of weighted [Formula: see text]-Changhee polynomials and [Formula: see text]-adic gamma function. Also, we compute the weighted fermionic [Formula: see text]-adic [Formula: see text]-integral of the derivative of [Formula: see text]-adic gamma function. Moreover, we give a novel representation for the [Formula: see text]-adic Euler constant by means of the weighted [Formula: see text]-Changhee polynomials and numbers. We finally provide a quirky explicit formula for [Formula: see text]-adic Euler constant.

On the degenerate (h,q)-Changhee numbers and polynomials

The Changhee numbers and polynomials are introduced by Kim, Kim and Seo (Adv. Stud. Theor. Phys. 7(20):993–1003, 2013), and the generalizations of those polynomials are characterized. In this paper, we investigate a new q-analog of the higher order degenerate Changhee polynomials and numbers. We derive some new interesting identities related to the degenerate (h,q)-Changhee polynomials and numbers.

Symmetry Identities of Changhee Polynomials of Type Two

In this paper, we consider Changhee polynomials of type two, which are motivated from the recent work of D. Kim and T. Kim. We investigate some symmetry identities for the Changhee polynomials of type two which are derived from the properties of symmetry for the fermionic p-adic integral on Z p .

On the <i>p</i>-adic Gamma Function and Changhee Polynomials

The p-adic gamma function is considered to obtain its derivative and to evaluate its the fermionic p-adic integral. Furthermore the relationship between the p-adic gamma function and Changhee polynomials and also between the Changhee polynomials and p-adic Euler constants is obtained. In addition, the p-adic Euler constants are expressed in term of Mahler coefficients of the p-adic gamma function.

Some Identities Involving the Higher-Order Changhee Numbers and Polynomials

In this paper, by the classical method of Riordan arrays, establish several general involving higher-order Changhee numbers and polynomials, which are related to special polynomials and numbers. From those numbers, we derive some interesting and new identities.

On modified degenerate Changhee polynomials and numbers

On modified degenerate Changhee polynomials and numbers

Some explicit identities on Changhee-Genocchi polynomials and numbers

In this paper, we introduce a new family of functions, which is called the Changhee-Genocchi polynomials. We study some explicit identities on these polynomials, which are related to Genocchi polynomials and Changhee polynomials. Also, we represent Changhee-Genocchi polynomials by gamma and beta functions. We also study some properties of higher-order Changhee-Genocchi polynomials related to Changhee polynomials and Daehee polynomials.

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.

Differential equations for Changhee polynomials and their applications

Recently, the non-linear Changhee differential equations were introduced in [5] and these differential equations turned out to be very useful for studying special polynomials and mathematical physics. Some interesting identities and properties of Changhee polynomials can also be derived from umbral calculus (see [7]). In this paper, we consider differential equations arising from Changhee polynomials and derive some new and explicit formulae and identities from our differential equations.

Some properties of the twisted Changhee polynomials and their zeros

Kim et al. [9] studied some special polynomials and numbers which are closely related to Changhee polynomials and numbers, and Park et al. (2014) [17] studied the twisted Changhee polynomials and numbers.In this paper we consider the twisted Changhee polynomials and numbers. From these polynomials and numbers, we derive some identities. Furthermore, we investigate the higher-order twisted Changhee polynomials and numbers and also discuss some computations of zeros of the twisted Changhee 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.

A note on Changhee polynomials and numbers with q-parameter

In this paper, we consider the q-extensions of Changhee polynomials which are derived from the fermionic p-adic integral on Zp and the q-analogue of falling factorial sequence. Finally, we give some identities of those polynomials.