Functions of One Complex Variable Special Part

Abstract

Let a ₀, a ₁, a ₂,..., a _n,... be complex numbers not all zero. Let the power series

$$ f(z) = a_0 + a_1 z + a_2 z^2 + \cdots + a_n z^n + \cdots $$

have radius of convergence R, R >0. If R=∞, f(z) is called an entire function.