Geodesic
Decomposition of a regular quaternion function
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 28 (2018) no. 1, pp. 36-47

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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, quaternion meromorphic function.
Mots-clés : Laurent series, residue 
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     title = {Decomposition of a regular quaternion function},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
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     url = {http://geodesic.mathdoc.fr/item/VUU_2018_28_1_a3/}
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I. S. Polyanskii; V. M. Radygin; S. Yu. Misyurin. Decomposition of a regular quaternion function. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 28 (2018) no. 1, pp. 36-47. http://geodesic.mathdoc.fr/item/VUU_2018_28_1_a3/