Weierstrass M-test

The Weierstrass majorant criterion (also: Weierstrass M- Test) is a criterion for the detection of uniform and absolute convergence of a series of functions. As a special case it contains the majorant criterion for series. It was named after the mathematician Karl Weierstrass.

Statement

Let be a sequence of complex-valued functions on real or the crowd. Be positive constants, so that

For all and all in applies. Furthermore, the series converges.

Then: The Series

Converges absolutely and uniformly on.