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.