1.) See here
2.) I suggest looking at the Laurent Series for f+g, fg, f/g
Hi all ,
please i need the solution of these question or at least Hints
[1] Let f(z) be entire function and assume that there exist M, R >0 and n positive integer such that |f(z)|≤M(|z|^n) for all z in C-D(0,R). Prove that f(z) is a polynomial of degee≤n.
[2] Suppose f and g have poles of order m and n respectively at z . Describe the singularity Of the following function at z :
f+g, fg and f/g .
Thanks all