ABSTRACT
Definition 1.1 Consider a fixed ξ0 ∈ F and constants aj ∈ F for j ≥ 0. A series of the form ∞∑
aj (ξ − ξ0) j ,
for ξ ∈ F is called a power series centered at ξ0. The radius of convergence of the power series is defined as
R ≡ sup { |ξ − ξ0| :
aj(ξ − ξ0) j converges
} ,
when the supremum exists. WhenR exists and is nonzero, the neighborhood NR(ξ0) is called the neighborhood of convergence.
