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Home » Issues » Archive of Issues » 2018 - 1 issue » pp. 36-47

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Russia Moscow
Year
2018
Volume
28
Issue
1
Pages
36-47
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Section Mathematics
Title Decomposition of a regular quaternion function
Author(-s) Polyanskii I.S.a, Radygin V.M.a, Misyurin S.Yu.b
Affiliations The Academy of Federal Security Guard Service of the Russian Federationa, National Research Nuclear University MEPhIb
Abstract This article deals with the tasks associated with the decomposition of a regular quaternion function into generalized Taylor and Laurent series. The generalized Taylor series for a regular quaternion function were obtained by the decomposition of the Cauchy kernel in a 4-dimensional hyperball in the algebra of quaternions and the hyperspherical coordinate system. The generalized Laurent series for a regular quaternion function were obtained by the decomposition of the Cauchy kernel in the exterior of a 4-dimensional hyperball in the algebra of quaternions and the hyperspherical coordinate system. On the basis of the obtained solutions by considering the decomposition of a regular quaternion function in an infinitely small ball that is restricted by the 3-sphere, we set the rule to determine the deduction of a regular quaternion function in the algebra of quaternions and the hyperspherical coordinate system regarding the isolated singular point. In addition, the decomposition of a meromorphic quaternion function into the power series was found.
Keywords regular quaternion function, Taylor series, Laurent series, residue, quaternion meromorphic function
UDC 517.554
MSC 30B10
DOI 10.20537/vm180104
Received 12 October 2017
Language Russian
Citation Polyanskii I.S., Radygin V.M., Misyurin S.Yu. Decomposition of a regular quaternion function, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2018, vol. 28, issue 1, pp. 36-47.
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