바로가기메뉴

본문 바로가기 주메뉴 바로가기

ACOMS+ 및 학술지 리포지터리 설명회

  • 한국과학기술정보연구원(KISTI) 서울분원 대회의실(별관 3층)
  • 2024년 07월 03일(수) 13:30
 

logo

  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

TAYLOR SERIES OF FUNCTIONS WITH VALUES IN DUAL QUATERNION

TAYLOR SERIES OF FUNCTIONS WITH VALUES IN DUAL QUATERNION

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2013, v.20 no.4, pp.251-258
https://doi.org/10.7468/jksmeb.2013.20.4.251
Kim, Ji Eun (Department of Mathematics, Pusan National University)
Lim, Su Jin (Department of Mathematics, Pusan National University)
Shon, Kwang Ho (Department of Mathematics, Pusan National University)

Abstract

We define an <TEX>${\varepsilon}$</TEX>-regular function in dual quaternions. From the properties of <TEX>${\varepsilon}$</TEX>-regular functions, we represent the Taylor series of <TEX>${\varepsilon}$</TEX>-regular functions with values in dual quaternions.

keywords
regular functions, Clifford analysis, dual quaternion, Taylor series

참고문헌

1.

(1873). Preliminary sketch of bi-quaternions (381-395). Proc. London Math. Soc..

2.

(1934). Die Fuktionentheorie der Defferentialgeleichungen <TEX>${\Delta}$</TEX>u = 0 und <TEX>${\Delta}{\Delta}$</TEX>u = 0 mit vier reellen Variablen. Comment. Math. Helv., 7, 307-330. 10.1007/BF01292723.

3.

(2012). Regular functions with values in a Commutative subalgebra <TEX>${\mathbb{C}}(<TEX>${\mathbb{C}}$</TEX>)$</TEX> of Matrix algebra M(4;<TEX>${\mathbb{R}}$</TEX>). Bull. Fukuoka Univ. Ed., 61, 9-15.

4.

(2012). A beginners guide to dual-quaternions: What they are, How they work, and How to use them for 3D character hierarchies (1-10). The 20th International Conf. on Computer Graphics, Visualization and Computer Vision.

5.

(2011). Hyperholomorphic Functions and Holomorphic functions in Quaternionic Analysis. Bull. Fukuoka Univ. Ed., 60, 1-9.

6.

Screw calculus and some applications to geometry and mechanics.

7.

(2013). Regularity of functions with values in a non-commutative algebra of complex matrix algebras. Sci. China Math., .

8.

(1971). Hyperholomorphic functions. Siberian Math. J., 12, 959-968.

9.

(1983). Hyperholomorphic functions of a quaternion variable. Bull. Fukuoka Univ. Ed., 32, 21-37.

10.

(1986). Characterization of domains of holomorphy by the existence of hyper-conjugate harmonic functions. Rev. Roumaine Math. Pures Appl., 31(2), 159-161.

11.

(1987). Domains of Hyperholomorphic in <TEX>${\mathbb{C}}^2{\times}{\mathbb{C}}^2$</TEX>. Bull. Fukuoka Univ. Ed., 36, 1-9.

12.

(1983). Complex Clifford Analysis. Complex Variables Theory Appl., 1, 119-149.

13.

(1983). Special functions and relations within complex Clifford analysis I. Complex Variables Theory Appl., 2, 177-198. 10.1080/17476938308814041.

14.

Geometrie der Dynamen.

15.

(1979). Quaternionic analysis. Math. Proc. Camb. Phil. Soc., 85, 199-225. 10.1017/S0305004100055638.

한국수학교육학회지시리즈B:순수및응용수학