The Laurent expansion and residue theorem of weighted monogenic functions

Abstract

ABSTRACTFirstly, the definition of p order homogeneous weighted right monogenic polynomials is given, and the hypercomplex variables are introduced in order to construct a basis of all homogeneous weighted right monogenic polynomials of degree p, then the second Taylor expansion of the weighted right monogenic functions is obtained. Secondly, the weighted left monogenic functions are constructed from continuous functions in different regions, and corresponding Taylor expansions are given. Finally, on the basis of the previous conclusions, the Laurent expansion and residue theorem of the weighted left monogenic functions are proved.KEYWORDS: Weighted monogenic functionsp order homogeneous weighted right monogenic polynomialshypercomplex variablesLaurent expansionresidue theoremAMS SUBJECT CLASSIFICATIONS: 30B1030G3532A05 Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis work was supported by the Natural Science Foundation of Hebei Province [grant numbers A2020205008 and A2015205012], Key Foundation of Hebei Normal University [grant number L2021Z01] and the National Natural Science Foundation of China [grant numbers 11401162, 11871191, and 11571089].