0.301 The series
the terms of which are functions, is called a functional series. The set of values of the independent variable x for which the series 0.301 1 converges constitutes what is called the region of convergence of that series.
0.302 A series that converges for all values of x in a region M is said to converge uniformly in that region if, for every e = 0, there exists a number N such that, for n > N, the inequality
holds for all x in M.