Weierstrass’ criterion of uniform convergence


Let the real functions f1(x), f2(x), … be defined in the interval [a,b].  If they all the condition


with n=1Mn a convergent seriesMathworldPlanetmathPlanetmath of , then the function series


converges uniformly (http://planetmath.org/SumFunctionOfSeries) on the interval [a,b].

The theorem is valid also for the series with complex function terms, when one replaces the interval with a subset of .

Title Weierstrass’ criterion of uniform convergenceMathworldPlanetmath
Canonical name WeierstrassCriterionOfUniformConvergence
Date of creation 2013-03-22 14:38:21
Last modified on 2013-03-22 14:38:21
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 9
Author pahio (2872)
Entry type Theorem
Classification msc 26A15
Classification msc 40A30
Synonym Weierstrass’ M-test