I need to frove the following (even some of those will help):
1. assume f(z) is an entire function [analytical on the whole plane], that holds for every n (natural) ==> if |z|=n^2 then |f(z)|<13. prove that f(z) is a constant function.
2. assume f(z) is a Meromorphic function [its finite singular points are only poles] on C, that holds for every z (complex) ==> f(z)=f(2f(z)). find all the functions f(z) [general form].
3. assume f(z) is periodical and analytical on a domain D that contains the point z=infinity. prove that f(z)=const on D.
4. assume f(z) is analytical on a bounded domain D, and continuous on D* (with the "boundary"). assume also that f is not constant on D, but |f| is constant on the "boundary". prove that f has a zero on D.
5. assume f(z) is analytical on a pierced surroundings of z=0 (sorry about the stammerer english, its not my mother tongue language...). prove that f(z) and h(z)=f(z+z^2) have the same "kind" of singular point on z=0, and if it is a zero or a pole, then the order is also the same.
TNX A LOT !!!