# Thread: Entire functions and polynomials. Poles and singularities.

1. ## Entire functions and polynomials. Poles and singularities.

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

2. Originally Posted by raed
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
1.) See here

2.) I suggest looking at the Laurent Series for f+g, fg, f/g

3. Originally Posted by chiph588@
1.) See here

2.) I suggest looking at the Laurent Series for f+g, fg, f/g
Thank u very much