Poles of regular quaternionic functions

Details Poles of regular quaternionic functions Poles of regular quaternionic functions

2008-04-10

arxiv.org/abs/0804.1665v1

Complex Var. Elliptic Equ., 54(11):1001--1018, 2009

Mathematics

Complex Variables

14 pages

Scientific paper

10.1080/17476930903275938

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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