Weierstrass’ criterion of uniform convergence
Theorem.
Let the real functions , , … be defined in the interval . If they all the condition
with a convergent series of , then the function series
converges uniformly (http://planetmath.org/SumFunctionOfSeries) on the interval .
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 convergence |
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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 |