Let be an entire function such that for all x, y,

and . Find f .

First I thought that working using Euler's notation would make the thing simpler. Let

The condition are thus

and .

Then where

. Since this is a composition of entire function it should be an entire function.

I'm not comfortable with complex variables so I ask for some help. The question suggest there might be a single but I [think I] found many. Does what is above makes any sense?