## You are here

HomeMittag-Leffler's theorem

## Primary tabs

# Mittag-Leffler’s theorem

Let $G$ be an open subset of $\mathbb{C}$, let $\{a_{k}\}$ be a sequence of distinct points in $G$ which has no limit point in $G$. For each $k$, let $A_{{1k}},\dots,A_{{m_{k}k}}$ be arbitrary complex coefficients, and define

$S_{k}(z)=\sum_{{j=1}}^{{m_{k}}}\frac{A_{{jk}}}{(z-a_{k})^{j}}.$ |

Then there exists a meromorphic function $f$ on $G$ whose poles are exactly the points $\{a_{k}\}$ and such that the singular part of $f$ at $a_{k}$ is $S_{k}(z)$, for each $k$.

Related:

WeierstrassFactorizationTheorem

Type of Math Object:

Theorem

Major Section:

Reference

## Mathematics Subject Classification

30D30*no label found*

- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)

- Other useful stuff