Regular part

In mathematics, the regular part of a Laurent series consists of the series of terms with positive powers.[1] That is, if

${\displaystyle f(z)=\sum _{n=-\infty }^{\infty }a_{n}(z-c)^{n},}$

then the regular part of this Laurent series is

${\displaystyle \sum _{n=0}^{\infty }a_{n}(z-c)^{n}.}$

In contrast, the series of terms with negative powers is the principal part.[1]

References

1. Jeffrey, Alan (2005), Complex Analysis and Applications (2nd ed.), CRC Press, p. 256, ISBN 9781584885535.