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uniformly convergent sequence

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  • 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

  • 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

  • Cauchy sequence — In mathematics, a Cauchy sequence, named after Augustin Cauchy, is a sequence whose elements become arbitrarily close to each other as the sequence progresses. To be more precise, by dropping enough (but still only a finite number of) terms from… …   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

  • 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

  • Riemann integral — In the branch of mathematics known as real analysis, the Riemann integral, created by Bernhard Riemann, was the first rigorous definition of the integral of a function on an interval. While the Riemann integral is unsuitable for many theoretical… …   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

  • 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

  • Hilbert space — For the Hilbert space filling curve, see Hilbert curve. Hilbert spaces can be used to study the harmonics of vibrating strings. The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space. It… …   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

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