Convergent Series - Uniform Convergence

Uniform Convergence

Main article: uniform convergence.

Let be a sequence of functions. The series is said to converge uniformly to f if the sequence of partial sums defined by

converges uniformly to f.

There is an analogue of the comparison test for infinite series of functions called the Weierstrass M-test.

Read more about this topic:  Convergent Series

Famous quotes containing the word uniform:

    “An accent mark, perhaps, instead of a whole western accent—a point of punctuation rather than a uniform twang. That is how it should be worn: as a quiet point of character reference, an apt phrase of sartorial allusion—macho, sotto voce.”
    —Phil Patton (b. 1953)