Talk:Mittag-Leffler's theorem

Imprecision in statement

If $p_{a}(z)$ is a polynomial in $1/(z-a)$, then it is $f(z)-p_{a}(z)$ that has only a removable singularity at $a$. Superhiggs (talk) 14:35, 17 November 2021 (UTC)

Bad proof outline

The article offered a proof outline:

Use Runge's theorem to construct a rational function $R_{F}(z)$ approximating $S_{F}(z)$. As $E$ is exhausted by the finite sets $F$, the approximations $R_{F}(z)$ will approach a limit, which is the desired meromorphic function $f$.

This is incorrect as the Runge's theorem approximations are not guaranteed to converge and in any case they don't have the correct principal parts. I've edited the article. 75.76.162.89 (talk) 05:02, 2 June 2012 (UTC)

Examples

The example in "Another example" has poles in Z, not Z⁺ — Preceding unsigned comment added by 18.111.25.135 (talk) 02:04, 17 June 2013 (UTC)