I have to find all holomorphic functions F(z)=F(x+iy)
F(x+iy)=P(x,y) + i Q(x,y)
with the condition (1) that P(x,y)/Q(x,y) is a function of x only.
Combining (1) with cauchy relations I reach that the module of F depends only on y. But I can't get more precise, though I think it must be possible.
Thanks for any help.