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:

    The sugar maple is remarkable for its clean ankle. The groves of these trees looked like vast forest sheds, their branches stopping short at a uniform height, four or five feet from the ground, like eaves, as if they had been trimmed by art, so that you could look under and through the whole grove with its leafy canopy, as under a tent whose curtain is raised.
    Henry David Thoreau (1817–1862)