regular part

{{Short description|(of a Laurent series) consists of the series of terms with positive powers}}

{{one source|date=April 2025}}

{{Use dmy dates|date=April 2025}}

In mathematics, the regular part of a Laurent series consists of the series of terms with positive powers.{{citation|title=Complex Analysis and Applications|first=Alan|last=Jeffrey|edition=2nd|publisher=CRC Press|year=2005|isbn=9781584885535|page=256|url=https://books.google.com/books?id=O039eVfuV04C&pg=PA256}}. That is, if

:$f(z)\; =\; \backslash sum\_\{n=-\backslash infty\}^\{\backslash infty\}\; a\_n\; (z\; -\; c)^n,$

then the regular part of this Laurent series is

:$\backslash sum\_\{n=0\}^\{\backslash infty\}\; a\_n\; (z\; -\; c)^n.$

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