where x is a variable, where {a_{n}} is a sequence and c is a constant, is called a power series about c (or centered at c).
We can define a function
In particular, the domain of F is the collection of those values of x for which the series is convergent. We note that c is in the domain of F.
Examples.
the domain of F is either
In case 2, R is called the radius of convergence. In case 1 and case 3, we say that the radius of convergence is 0 and ¥, respectively.
The domain of F is generally referred to as the interval of convergence.