Talk:Meromorphic function

must the set of poles be finite? -- Tarquin

Nope. 1/sin(z) is meromorphic. AxelBoldt

how big can the set of poles be

I don't think I completely understand the definition.

Can there be an infinite amount of poles? And if so, do they have to be countable? --anon

Yes, they can be an infinite set. Hopefully my rewrite shows that.

They really do have to be isolated? --anon Yes, by definition. If they are not isolated, it is impossible to prove that a meromorphic function is a ratio of two holomorphic functions. Oleg Alexandrov 17:28, 11 August 2005 (UTC)[reply]

the amount of poles of a meromorphic function must not be countable?

http://mathworld.wolfram.com/MeromorphicFunction.html

here they speak of

if this a different definition or is it some non trivial theorem that if your definition is true, the number of poles is countable

thanks