Regular part

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

f ( z ) = ∑ n = − ∞ ∞ a n ( z − c ) n , {\displaystyle f(z)=\sum _{n=-\infty }^{\infty }a_{n}(z-c)^{n},}

then the regular part of this Laurent series is

∑ n = 0 ∞ a n ( z − c ) n . {\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. ^ a b Jeffrey, Alan (2005), Complex Analysis and Applications (2nd ed.), CRC Press, p. 256, ISBN 9781584885535.


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