In 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 ...

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