The Laurent expansion and residue theorem of weighted monogenic functions

Firstly, 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.

Automated summary

The definition of p order homogeneous weighted right monogenic polynomials is given, and hypercomplex variables are introduced to construct a basis for all p degree homogeneous weighted right monogenic polynomials. The second Taylor expansion of the weighted right monogenic functions is obtained. In addition, weighted left monogenic functions are constructed from continuous functions in different regions and corresponding Taylor expansions are given. Finally, the Laurent expansion and residue theorem of the weighted left monogenic functions are proved based on the previous conclusions.