Regular part
Encyclopedia
In mathematics
, the regular part of a Laurent series
consists of the series of terms with positive powers. That is, if
then the regular part of this Laurent series is
In contrast, the series of terms with negative powers is the principal part
.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, the regular part of a Laurent series
Laurent series
In mathematics, the Laurent series of a complex function f is a representation of that function as a power series which includes terms of negative degree. It may be used to express complex functions in cases where...
consists of the series of terms with positive powers. That is, if
then the regular part of this Laurent series is
In contrast, the series of terms with negative powers is the principal part
Principal part
In mathematics, the principal part has several independent meanings, but usually refers to the negative-power portion of the Laurent series of a function.-Laurent series definition:...
.