Hi all, I need the solution of the following problem
[1] Use Liouville’s theorem to prove that a non-constant polynomial cannot satisfy f(z+1) = f(z) and f(z+i) = f(z) for all z.
Thank for all
Hi all, I need the solution of the following problem
[1] Use Liouville’s theorem to prove that a non-constant polynomial cannot satisfy f(z+1) = f(z) and f(z+i) = f(z) for all z.
Thank for all
How's this?
Note by induction and combining these two . So, given we may note that (fractional and integer part). So, letting we see that an thus is entirely determined on but this region is clearly compact and thus being continuous is bounded on it. Thus, by previous remarks it follows that is bounded on and so
I don't see why this works for any entire function though?