Principal part

In mathematics, the principal part of the Laurent series of a function f(z),

$\sum_{k=-\infty}^\infty a_k (z-a)^k$

is the series of terms with negative degree, that is

$\sum_{k=-\infty}^{-1} a_k (z-a)^k$

Say f(z) has an essential singularity at p. Then, the principal part is an infinite sum, and vice versa.

The term principal part is also used in distribution theory, for certain kinds of distribution having a singular support at a single point.

External link

Last updated: 10-11-2005 13:15:50