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arXiv · 0804.1665

Poles of regular quaternionic functions

Caterina Stoppato
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Abstract

This paper studies the singularities of Cullen-regular functions of one quaternionic variable. The quaternionic Laurent series prove to be Cullen-regular. The singularities of Cullen-regular functions are thus classified as removable, essential or poles. The quaternionic analogues of meromorphic complex functions, called semiregular functions, turn out to be quotients of Cullen-regular functions with respect to an appropriate division operation. This allows a detailed study of the poles and their distribution.

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Caterina Stoppato. 2008-04-10. Poles of regular quaternionic functions. https://doi.org/10.1080/17476930903275938

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