The power series represents a continuous function in its domain of convergence (the end-points may have to be excluded).
The theory of power series has been developed chiefly from the point of view of the theory of functions of complex variables.
A power series converges uniformly in any interval contained within its domain of convergence, the end-points being excluded.
|power series |
A sum of successively higher integral powers of a variable or combination of variables, each multiplied by a constant coefficient.