Question: Finding complex roots in polynomial of infinite order

Hi guys,

I am trying to solve for the roots in a polynomial of infinite order. The idea is simply to approximate the infinite polynomial by a high order Taylor expansion, solve for the roots in this polynomial (both real and complex roots exists) and use these roots as initial guesses for finding the authentic roots of the infinite polynomial in this specific range.

I have tried to use the evalf(RootOf(PolyInfinite=0,x,Re + Im)), however the output from RootOf seems to converge to the same 2 or 3 roots almost independent of the initial guess. Is there specific options of this RootOf function that can stabilize the solution or another/better command to use?

On the other hand i could solve this by simply minimizing a least sqaure, however i have not found any optimization solver which supports solutions in the complex domain?

I sincerely hope that you are able to help me.

Kind regards

Lasse