Can we get a function whose infinite series is in the form: $g(z) = 1 + z + 2z^2 + 3z^3 + 5z^4 + 8z^5 + 13z^6 + ... $ Or $f(z) = g(z)-1 = z + 2z^2 + 3z^3 + 5z^4 + 8z^5 + 13z^6 + ...$
where $z$ is a complex number and the coefficients are the terms of the popular Fibonacci sequence?
