Weierstrass M-test
In mathematics, the Weierstrass M-test is an analogue of the comparison test for infinite series, and applies to a series whose terms are themselves functions of a real variable.
Suppose  is a sequence of complex-valued functions defined on a subset  , and that for some fixed positive integer N, there exist positive constants  such that
for all  and all  . Suppose further that the series
converges. Then, the series
converges uniformly on  . (See uniform convergence.)
A more general version of the Weierstrass M-test holds if the codomain of the functions is any Banach space, in which case the statement
may be replaced by
 ,
where  is the norm afforded by the Banach space.
Referenced By
Karl Weierstrass | Karl Weierstraß | Weierstrass
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