## Definition 8.3.1: Function Series

Suppose

*{ f*is a sequence of functions and we define the N-th partial sum as_{n}(x) }LetS_{N}(x) = f_{n}(x)

*be the set of points for which the sequence of partial sums converges pointwise. Then, for***D***x*, we denote the resulting limit function by**D**f_{n}(x) = S_{N}(x) = f_{n}(x)