Se0g-Hoon Rim - Academia.edu (original) (raw)

Papers by Se0g-Hoon Rim

Research paper thumbnail of a Department of Mathematics Education, Kyungpook National University

Abstract: In the recent paper, Kim-Rim have studied interesting twisted q-Euler numbers and polyn... more Abstract: In the recent paper, Kim-Rim have studied interesting twisted q-Euler numbers and polynomials. In [8], Kim-Rim suggested the question to find a q-analogue of the p-adic twisted (h, q)-l-function which interpolates generalized twisted (h, q)-Euler numbers attached to χ. This question is remained open. The purpose of this paper is to give the answer of the question. 1.

Research paper thumbnail of Bernstein polynomials on Simplex

We prove two identities for multivariate Bernstein polynomials on simplex, which are considered o... more We prove two identities for multivariate Bernstein polynomials on simplex, which are considered on a pointwise. In this paper, we study good approximations of Bernstein polynomials for every continuous functions on simplex and the higher dimensional q-analogues of Bernstein polynomials on simplex

Research paper thumbnail of On the associated sequence of special polynomials

Advanced Studies in Contemporary Mathematics (Kyungshang)

In this paper, we investigate some properties of the associated sequence of Daehee and Changhee p... more In this paper, we investigate some properties of the associated sequence of Daehee and Changhee polynomials. Finally, we give some interesting identities of associated sequence involving some special polynomials.

Research paper thumbnail of A note on p-adic q-Euler measure

In this paper we will investigate properties of modified q-Euler numbers and polynomials. The mai... more In this paper we will investigate properties of modified q-Euler numbers and polynomials. The main purpose of this paper is to construct p-adic q-Euler measures.

Research paper thumbnail of Daehee Formula Associated with the q-Extensions of Trigonometric Functions

In this paper we introduce a Daehee constant which is called q-extension of Napier constant, and ... more In this paper we introduce a Daehee constant which is called q-extension of Napier constant, and consider Daehee formula associated with the qextensions of trigonometric functions. That is, we derive the q-extensions of sine and cosine functions from this Daehee formula. Finally, we give the q-calculus related to the q-extensions of sine and cosine functions.

Research paper thumbnail of A note on p-adic Euler measure on ℤp

Russian Journal of Mathematical Physics, 2006

ABSTRACT In this paper, we give some p-adic approximation of E n,x for certain n. Finally we will... more ABSTRACT In this paper, we give some p-adic approximation of E n,x for certain n. Finally we will treat p-adic l-function of Kubota-Leopoldt’s type Euler numbers and p-adic measure for Euler numbers.

Research paper thumbnail of Extended q-euler numbers and polynomials associated with fermionic p-adic q-integral on Z p

Russian Journal of Mathematical Physics, 2007

The purpose of this paper is to construct new q-Euler numbers and polynomials. Finally we will co... more The purpose of this paper is to construct new q-Euler numbers and polynomials. Finally we will consider the Witt's type formula associated with these q-Euler numbers and polynomials, and construct q-partial zeta functions and p-adic q-l-functions which interpolate new q-Euler numbers and polynomials at negative integers.

Research paper thumbnail of q-Euler numbers and polynomials associated with p-adic q-integrals

Journal of Nonlinear Mathematical Physics, 2007

The main purpose of this paper is to present a systemic study of some families of multiple q-Eule... more The main purpose of this paper is to present a systemic study of some families of multiple q-Euler numbers and polynomials. In particular, by using the q-Volkenborn integration on Z p , we construct p-adic q-Euler numbers and polynomials of higher order. We also define new generating functions of multiple q-Euler numbers and polynomials. Furthermore, we construct Euler q-Zeta function. Over five decades ago, Calitz [2, 3] defined q-extension of Frobenius-Euler numbers and polynomials and proved properties analogous to those satisfied H n (u) and H n (u, x). Recently, Satoh [14, 15] used these properties, especially the so-called distribution relation

Research paper thumbnail of An invariant p-adic q-integral associated with q-Euler numbers and polynomials

Journal of Nonlinear Mathematical Physics, 2007

The purpose of this paper is to consider q-Euler numbers and polynomials which are q-extensions o... more The purpose of this paper is to consider q-Euler numbers and polynomials which are q-extensions of ordinary Euler numbers and polynomials by the computations of the p-adic q-integrals due to T. Kim, cf. [1, 3, 6, 12], and to derive the "complete sums for q-Euler polynomials" which are evaluated by using multivariate p-adic q-integrals. These sums help us to study the relationships between p-adic q-integrals and nonarchimedean combinatorial analysis.

Research paper thumbnail of A note on the q-integral and q-series

Advanced Studies in Contemporary Mathematics (Kyungshang)

Research paper thumbnail of An explicit formula for the multiple Frobenius-Euler numbers and polynomials

JP Journal of Algebra, Number Theory and Applications

Research paper thumbnail of Q-Analogue of the P-Adic Twisted L-Function

Research paper thumbnail of Proceedings of the 15th International Conference on Oral Chelation (ICOC) in the Treatment of Thalassemia and Other Diseases. Part 1. Taichung, Taiwan. April 22-26, 2005

Research paper thumbnail of A note on the sums of powers of consecutive q-integers

ABSTRACT In this paper we construct the q-analogue of Barnes' Bernoulli numbers and plyno... more ABSTRACT In this paper we construct the q-analogue of Barnes' Bernoulli numbers and plynomials of degree 2, which is an answer to a part of Schlosser's question. Finally, we treat the q-analogue of the sums of powers of consecutive integrs.

Research paper thumbnail of On the twisted <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>q</mi></mrow><annotation encoding="application/x-tex">q</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">q</span></span></span></span>-zeta functions and <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>q</mi></mrow><annotation encoding="application/x-tex">q</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">q</span></span></span></span>Bernoulli polynomials

We study the twisted q-zeta functions and twisted q-Bernoulli polynomials

Research paper thumbnail of An extension of q-zeta function

International Journal of Mathematics and Mathematical Sciences, 2004

Research paper thumbnail of Exploring the sums of powers of consecutive q -integers

International Journal of Mathematical Education in Science and Technology, 2005

ABSTRACT Let n, k be positive integers (k &gt; 1), and let Sn,q(k) be the sums of the nth pow... more ABSTRACT Let n, k be positive integers (k &gt; 1), and let Sn,q(k) be the sums of the nth powers of positive q-integers up to k − 1: , where [l]q=(q −1/q−1). Following an idea due to J. Bernoulli, we explore a formula for Sn,q(k) as follows: where βi,q are the q-Bernoulli numbers.

Research paper thumbnail of Exploring the q-Riemann zeta function and q-Bernoulli polynomials

Discrete Dynamics in Nature and Society, 2005

We study that the q-Bernoulli polynomials, which were constructed by Kim, are analytic continued ... more We study that the q-Bernoulli polynomials, which were constructed by Kim, are analytic continued to β s (z). A new formula for the q-Riemann zeta function ζ q (s) due to Kim in terms of nested series of ζ q (n) is derived. The new concept of dynamics of the zeros of analytic continued polynomials is introduced, and an interesting phenomenon of "scattering" of the zeros of β s (z) is observed. Following the idea of q-zeta function due to Kim, we are going to use "Mathematica" to explore a formula for ζ q (n). for x, q ∈ C (cf. ).

Research paper thumbnail of A note on p-adic q-Euler measure

In this paper we will investigate properties of modified q-Euler numbers and polynomials. The mai... more In this paper we will investigate properties of modified q-Euler numbers and polynomials. The main purpose of this paper is to construct p-adic q-Euler measures.

Research paper thumbnail of a Department of Mathematics Education, Kyungpook National University

Abstract: In the recent paper, Kim-Rim have studied interesting twisted q-Euler numbers and polyn... more Abstract: In the recent paper, Kim-Rim have studied interesting twisted q-Euler numbers and polynomials. In [8], Kim-Rim suggested the question to find a q-analogue of the p-adic twisted (h, q)-l-function which interpolates generalized twisted (h, q)-Euler numbers attached to χ. This question is remained open. The purpose of this paper is to give the answer of the question. 1.

Research paper thumbnail of Bernstein polynomials on Simplex

We prove two identities for multivariate Bernstein polynomials on simplex, which are considered o... more We prove two identities for multivariate Bernstein polynomials on simplex, which are considered on a pointwise. In this paper, we study good approximations of Bernstein polynomials for every continuous functions on simplex and the higher dimensional q-analogues of Bernstein polynomials on simplex

Research paper thumbnail of On the associated sequence of special polynomials

Advanced Studies in Contemporary Mathematics (Kyungshang)

In this paper, we investigate some properties of the associated sequence of Daehee and Changhee p... more In this paper, we investigate some properties of the associated sequence of Daehee and Changhee polynomials. Finally, we give some interesting identities of associated sequence involving some special polynomials.

Research paper thumbnail of A note on p-adic q-Euler measure

In this paper we will investigate properties of modified q-Euler numbers and polynomials. The mai... more In this paper we will investigate properties of modified q-Euler numbers and polynomials. The main purpose of this paper is to construct p-adic q-Euler measures.

Research paper thumbnail of Daehee Formula Associated with the q-Extensions of Trigonometric Functions

In this paper we introduce a Daehee constant which is called q-extension of Napier constant, and ... more In this paper we introduce a Daehee constant which is called q-extension of Napier constant, and consider Daehee formula associated with the qextensions of trigonometric functions. That is, we derive the q-extensions of sine and cosine functions from this Daehee formula. Finally, we give the q-calculus related to the q-extensions of sine and cosine functions.

Research paper thumbnail of A note on p-adic Euler measure on ℤp

Russian Journal of Mathematical Physics, 2006

ABSTRACT In this paper, we give some p-adic approximation of E n,x for certain n. Finally we will... more ABSTRACT In this paper, we give some p-adic approximation of E n,x for certain n. Finally we will treat p-adic l-function of Kubota-Leopoldt’s type Euler numbers and p-adic measure for Euler numbers.

Research paper thumbnail of Extended q-euler numbers and polynomials associated with fermionic p-adic q-integral on Z p

Russian Journal of Mathematical Physics, 2007

The purpose of this paper is to construct new q-Euler numbers and polynomials. Finally we will co... more The purpose of this paper is to construct new q-Euler numbers and polynomials. Finally we will consider the Witt's type formula associated with these q-Euler numbers and polynomials, and construct q-partial zeta functions and p-adic q-l-functions which interpolate new q-Euler numbers and polynomials at negative integers.

Research paper thumbnail of q-Euler numbers and polynomials associated with p-adic q-integrals

Journal of Nonlinear Mathematical Physics, 2007

The main purpose of this paper is to present a systemic study of some families of multiple q-Eule... more The main purpose of this paper is to present a systemic study of some families of multiple q-Euler numbers and polynomials. In particular, by using the q-Volkenborn integration on Z p , we construct p-adic q-Euler numbers and polynomials of higher order. We also define new generating functions of multiple q-Euler numbers and polynomials. Furthermore, we construct Euler q-Zeta function. Over five decades ago, Calitz [2, 3] defined q-extension of Frobenius-Euler numbers and polynomials and proved properties analogous to those satisfied H n (u) and H n (u, x). Recently, Satoh [14, 15] used these properties, especially the so-called distribution relation

Research paper thumbnail of An invariant p-adic q-integral associated with q-Euler numbers and polynomials

Journal of Nonlinear Mathematical Physics, 2007

The purpose of this paper is to consider q-Euler numbers and polynomials which are q-extensions o... more The purpose of this paper is to consider q-Euler numbers and polynomials which are q-extensions of ordinary Euler numbers and polynomials by the computations of the p-adic q-integrals due to T. Kim, cf. [1, 3, 6, 12], and to derive the "complete sums for q-Euler polynomials" which are evaluated by using multivariate p-adic q-integrals. These sums help us to study the relationships between p-adic q-integrals and nonarchimedean combinatorial analysis.

Research paper thumbnail of A note on the q-integral and q-series

Advanced Studies in Contemporary Mathematics (Kyungshang)

Research paper thumbnail of An explicit formula for the multiple Frobenius-Euler numbers and polynomials

JP Journal of Algebra, Number Theory and Applications

Research paper thumbnail of Q-Analogue of the P-Adic Twisted L-Function

Research paper thumbnail of Proceedings of the 15th International Conference on Oral Chelation (ICOC) in the Treatment of Thalassemia and Other Diseases. Part 1. Taichung, Taiwan. April 22-26, 2005

Research paper thumbnail of A note on the sums of powers of consecutive q-integers

ABSTRACT In this paper we construct the q-analogue of Barnes&#39; Bernoulli numbers and plyno... more ABSTRACT In this paper we construct the q-analogue of Barnes&#39; Bernoulli numbers and plynomials of degree 2, which is an answer to a part of Schlosser&#39;s question. Finally, we treat the q-analogue of the sums of powers of consecutive integrs.

Research paper thumbnail of On the twisted <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>q</mi></mrow><annotation encoding="application/x-tex">q</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">q</span></span></span></span>-zeta functions and <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>q</mi></mrow><annotation encoding="application/x-tex">q</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">q</span></span></span></span>Bernoulli polynomials

We study the twisted q-zeta functions and twisted q-Bernoulli polynomials

Research paper thumbnail of An extension of q-zeta function

International Journal of Mathematics and Mathematical Sciences, 2004

Research paper thumbnail of Exploring the sums of powers of consecutive q -integers

International Journal of Mathematical Education in Science and Technology, 2005

ABSTRACT Let n, k be positive integers (k &gt; 1), and let Sn,q(k) be the sums of the nth pow... more ABSTRACT Let n, k be positive integers (k &gt; 1), and let Sn,q(k) be the sums of the nth powers of positive q-integers up to k − 1: , where [l]q=(q −1/q−1). Following an idea due to J. Bernoulli, we explore a formula for Sn,q(k) as follows: where βi,q are the q-Bernoulli numbers.

Research paper thumbnail of Exploring the q-Riemann zeta function and q-Bernoulli polynomials

Discrete Dynamics in Nature and Society, 2005

We study that the q-Bernoulli polynomials, which were constructed by Kim, are analytic continued ... more We study that the q-Bernoulli polynomials, which were constructed by Kim, are analytic continued to β s (z). A new formula for the q-Riemann zeta function ζ q (s) due to Kim in terms of nested series of ζ q (n) is derived. The new concept of dynamics of the zeros of analytic continued polynomials is introduced, and an interesting phenomenon of "scattering" of the zeros of β s (z) is observed. Following the idea of q-zeta function due to Kim, we are going to use "Mathematica" to explore a formula for ζ q (n). for x, q ∈ C (cf. ).

Research paper thumbnail of A note on p-adic q-Euler measure

In this paper we will investigate properties of modified q-Euler numbers and polynomials. The mai... more In this paper we will investigate properties of modified q-Euler numbers and polynomials. The main purpose of this paper is to construct p-adic q-Euler measures.