## Uniform Convergence

A Series is uniformly convergent to for a set of values of if, for each , an Integer can be found such that

 (1)

for and all . To test for uniform convergence, use Abel's Uniform Convergence Test or the Weierstraß M-Test. If individual terms of a uniformly converging series are continuous, then
1. The series sum
 (2)

is continuous,

2. The series may be integrated term by term
 (3)

and

3. The series may be differentiated term by term
 (4)