uniformly convergent

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• Convergent series — redirects here. For the short story collection, see Convergent Series (short story collection). In mathematics, a series is the sum of the terms of a sequence of numbers. Given a sequence , the nth partial sum Sn is the sum of the first n terms… …   Wikipedia

• Almost convergent sequence — A bounded real sequence (x n) is said to be almost convergent to L if each Banach limit assignsthe same value L to the sequence (x n).Lorentz proved that (x n) is almost convergent if and only if:limlimits {p oinfty} frac{x {n}+ldots+x {n+p… …   Wikipedia

• Uniform convergence — In the mathematical field of analysis, uniform convergence is a type of convergence stronger than pointwise convergence. A sequence {fn} of functions converges uniformly to a limiting function f if the speed of convergence of fn(x) to f(x) does… …   Wikipedia

• Uniform absolute-convergence — In mathematics, uniform absolute convergence is a type of convergence for series of functions. Like absolute convergence, it has the useful property that it is preserved when the order of summation is changed. Motivation A convergent series of… …   Wikipedia

• Series (mathematics) — A series is the sum of the terms of a sequence. Finite sequences and series have defined first and last terms, whereas infinite sequences and series continue indefinitely.[1] In mathematics, given an infinite sequence of numbers { an } …   Wikipedia

• Normal convergence — In mathematics normal convergence is a type of convergence for series of functions. Like absolute convergence, it has the useful property that it is preserved when the order of summation is changed. Contents 1 History 2 Definition 3 Distinctions …   Wikipedia

• Generalized continued fraction — In analysis, a generalized continued fraction is a generalization of regular continued fractions in canonical form in which the partial numerators and the partial denominators can assume arbitrary real or complex values.A generalized continued… …   Wikipedia

• Euler's continued fraction formula — In the analytic theory of continued fractions, Euler s continued fraction formula is an identity connecting a certain very general infinite series with an infinite continued fraction. First published in 1748, it was at first regarded as a simple… …   Wikipedia

• Compact space — Compactness redirects here. For the concept in first order logic, see compactness theorem. In mathematics, specifically general topology and metric topology, a compact space is an abstract mathematical space whose topology has the compactness… …   Wikipedia

• Pointwise convergence — In mathematics, pointwise convergence is one of various senses in which a sequence of functions can converge to a particular function.[1][2] Contents 1 Definition 2 Properties …   Wikipedia

• Equicontinuity — In mathematical analysis, a family of functions is equicontinuous if all the functions are continuous and they have equal variation over a given neighbourhood (a precise definition appears below). More generally, equicontinuous applies to any… …   Wikipedia