Archive
Special Issues Volume 6, Issue 3, June 2020, Page: 39-45
The Cauchy Integral Formula for Biregular Function in Octonionic Analysis
Yonghua Guo, School of Science, Tianjin University of Technology and Education, Tianjin, China
Haiyan Wang, School of Science, Tianjin University of Technology and Education, Tianjin, China
Received: Jul. 8, 2020;       Accepted: Aug. 21, 2020;       Published: Aug. 31, 2020
Abstract
In this paper, we mainly study the Cauchy integral formula and mean value theorem for biregular function in octonionic analysis. Octonion is the extension of complex number to non-commutative and non-associative space. Because of the non-associative properties of multiplication, octonion plays an important role in wave equation, Yang-Mills equations, operator theory and so on. In recent years, octonion has become a hot topic for scholars at home and abroad and got many rich results, such as Fourier transform, Bergman kernel, Taylor series and its applications in quantum mechanics. On the basis of two Stokes theorems, we get Cauchy integral formula for biregular function in octonionic analysis by using the methods in dealing with the Cauchy integral formula for biregular function in Clifford analysis and regular function in octonionic analysis. As a direct result we also get the mean value theorem for biregular function in octonionic analysis. This will generalize the corresponding conclusion in complex analysis and Clifford analysis, and lays a solid foundation for the application of octonionic analysis in physics.
Keywords
Octonion, Biregular Function, Cauchy Integral Formula, Mean Value Theorem
Yonghua Guo, Haiyan Wang, The Cauchy Integral Formula for Biregular Function in Octonionic Analysis, International Journal of Theoretical and Applied Mathematics. Vol. 6, No. 3, 2020, pp. 39-45. doi: 10.11648/j.ijtam.20200603.12
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