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

ISSN : 1226-0657

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Vol.20 No.4

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TAYLOR SERIES OF FUNCTIONS WITH VALUES IN DUAL QUATERNION

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / 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
Lim, Su Jin
Shon, Kwang Ho
Kim,, J. E. , Lim,, S. J. , & Shon,, K. H. (2013). TAYLOR SERIES OF FUNCTIONS WITH VALUES IN DUAL QUATERNION. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 20(4), 251-258, https://doi.org/10.7468/jksmeb.2013.20.4.251

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

Reference

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.

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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