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Taekyun Kim

Publications and source records attributed to Taekyun Kim.

At least 271 records · Page 15Linked to original sources
arXiv2007

Note on q-extensions of Euler numbers and polynomials of higher order

In [14] Ozden-Simsek-Cangul constructed generating functions of higher-order twisted $(h,q)$-extension of Euler polynomials and numbers, by using $p$-adic q-deformed fermionic integral on $\Bbb Z_p$. By applying their generating functions, they derived the complete sums of products of the twisted $(h,q)$-extension of Euler polynomials and numbers, see[13, 14]. In this paper we cosider the new $q$-extension of Euler numbers and polynomials to be different which is treated by Ozden-Simsek-Cangul. From our $q$-Euler numbers and polynomials we derive some interesting identities and we construct $q$-Euler zeta functions which interpolate the new $q$-Euler numbers and polynomials at a negative integer. Furthermore we study Barnes' type $q$-Euler zeta functions. Finally we will derive the new formula for " sums products of $q$-Euler numbers and polynomials" by using fermionic $p$-adic $q$-integral on $\Bbb Z_p$.

math.NT↗
arXiv2007

q-Bernoulli numbers and Stirling numbers(2)

In this paper we study q-Bernoulli numbers and polynomials related to q-Stirling numbers. From thsese studying we investigate some interesting q-stirling numbers' identities related to q-Bernoulli numbers.

math.NT↗
arXiv2007

Carlitz q-Bernoulli numbers and q-Stirling numbers

In this paper we consider carlitz q-Bernoulli numbers and q-stirling numbers of the first and the second kind. From these numbers we derive many interesting formulae associated with q-Bernoulli numbers.

math.NT↗
arXiv2006

A New Changhee q-Euler Numbers and Polynomials Associated with p-Adic q-Integrals

Using non-archimedean q-integrals on Zp defined in [15, 16], we define a new Changhee q-Euler polynomials and numbers which are different from those of Kim [7] and Carlitz [2]. We define generating functions of multiple q-Euler numbers and polynomials. Furthermore we construct multivariate Hurwitz type zeta function which interpolates the multivariate q-Euler numbers or polynomials at negative integers.

math.NT↗
arXiv2006

p-adic q-expansion of alternating sums of powers

In this paper, we will study p-adic q-expansion of alternating sums of powers. From these properties, we derive some interesting properties related to p-adic q-expansion of alternating sums of powers

math.NT↗
arXiv2006

A note on q-Euler numbers and polynomials

The purpose of this paper is to construct q-Euler numbers and polynomials by using p-adic q-integral equations on Zp. Finally, we will give some interesting formulae related to these q-Euler numbers and polynomials.

math.NT↗
arXiv2006

An Invarian p-adic q-integral on the rings of p-adic integers

In the recent p-adic q-integral on the p-adic integers' rings was constructed >. The purpose of this paper is to give several interesting integral equation for the p-adic q-integerals on the rings of p-adic integers. As an integral equations, we will treat relations between p-adic q-integral's equations and q-Bernoulli and Euler numbers.

math.NT↗
arXiv2006

A Note on p-Adic Invariant Integral in the Rings of p-Adic Integers

In [2], I constructed the p-adic q-integral on Zp. In this paper, we consider the properties of the p-adic invariant p-adic q-integral in the ring of p-adic integers at q=-1. Finally we give the some applications of p-adic q-integration at q=-1. These properties are useful and worthwhile to study Euler numbers and polynomials.

math.NT↗
arXiv2006

On p-adic q-l-functions and sums of powers

The purpose of this paper is to construct p-adic analytically continued function which interpolates q-Euler numbers at negative integer Finally, we give an explicit p-adic expansion as a power series in n.

math.NT↗
arXiv2005

A note on the Fourier transform of p-adic q-integral

The $p$-adic $q$-integral (= $I_q$-integral) was defined by author in the previous paper [1, 3]. In this paper, we consider $I_q$-Fourier transform and investigate some properties which are related to this transform.

math.NT↗