periodic equation

[tommy1729]

let f(z) and g(z) be real entire functions.

assuming a solution exists ( criterion ? )

for a given g(x) , all real x and any integer N :

f(x) = f(x + N * (g^2(x^2) + 1) i)

how to solve this ?

are simple pairs of f(x),g(x) known ?


regards

tommy1729