Talk:Casorati–Weierstrass theorem

Felice Casorati, as described in his article, was a painter. Did he really develop this theorem, or is another Felice Casorati meant? --Abdull 13:49, 10 June 2006 (UTC)[reply]

It appears that there were 2 of them - http://www-groups.dcs.st-and.ac.uk/history/Mathematicians/Casorati.html seems to be the mathematician. Madmath789 13:58, 10 June 2006 (UTC)[reply]

Is there a mistake in the first paragraph? Is it me or should that be |z-z_0| < delta, not epsilon? —Preceding unsigned comment added by 81.178.252.98 (talk) 23:32, 21 January 2008 (UTC)[reply]

There's no mistake. To be absolutely pedantic, one should say that for every complex number w and for every positive epsilon, there exists a complex z0 and a positive delta such that |f(z)-w|<epsilon for all z such that |z-z0|<delta. But the theorem is just as well stated if we put delta=epsilon (the statement is more clear to read and it remains correct). This is what the article does and that is why there is no typo. —Preceding unsigned comment added by 132.230.30.117 (talk) 14:45, 6 November 2009 (UTC)[reply]

This is all wrong. I'm correcting it now. —Preceding unsigned comment added by 131.111.139.100 (talk) 17:01, 27 October 2010 (UTC)[reply]

Why this is a theorem in complex analysis and not a characterization of meromorphic functions.

The Casorati-Sokhotskii-Weierstrass theorem deals with essential singularities of holomorphic functions: it is not a statement on the theory of Meromorphic functions since the singularities involved are not poles, and its aim is to study exactly the behavior of functions near such singularities, therefore outside their domain of meromorphy (see also the third example). Therefore I reverted the last two category changes simply because their are not correct nor on a mathematical basis nor on a classification basis. Daniele.tampieri (talk) 09:32, 19 July 2012 (UTC)[reply]

In the case that f is an entire function and a=\infty, ... -- but there is no 'a'

The last paragraph of the first section start with:

"In the case that f {\displaystyle f} f is an entire function and a = ∞ {\displaystyle a=\infty } a=\infty, the theorem says that the values f ( z ) {\displaystyle f(z)} f(z) approach every complex number and ∞ {\displaystyle \infty } \infty , as z {\displaystyle z} z tends to infinity."

but as far as I can see there is no mention of any 'a' before. 130.79.10.22 (talk) 09:16, 7 February 2019 (UTC)[reply]