mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

, the regular part of a

Laurent series In mathematics, the Laurent series of a complex function f(z) 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 a Taylor series expansion c ...

consists of the series of terms with positive powers.. That is, if :

f(z) = \sum_^ a_n (z - c)^n,

then the regular part of this Laurent series is :

\sum_^ a_n (z - c)^n.

In contrast, the series of terms with negative powers is the

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 The principal part at z=a of a function : f(z) = \sum_^\infty a_k ...

References

Complex analysis {{mathanalysis-stub