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Abel's test, the Glossary

In mathematics, Abel's test (also known as Abel's criterion) is a method of testing for the convergence of an infinite series.^[1]

18 relations: Addison-Wesley, Alternating series test, Complex analysis, Continuous function, Convergent series, Crelle's Journal, Dirichlet's test, Function (mathematics), Improper integral, Mathematics, Niels Henrik Abel, Power series, Radius of convergence, Series (mathematics), Summation by parts, Uniform boundedness, Uniform convergence, Unit circle.
Convergence tests

Addison-Wesley

Addison–Wesley is an American publisher of textbooks and computer literature.

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In mathematical analysis, the alternating series test is the method used to show that an alternating series is convergent when its terms (1) decrease in absolute value, and (2) approach zero in the limit. Abel's test and alternating series test are convergence tests.

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Complex analysis

Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers.

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Continuous function

In mathematics, a continuous function is a function such that a small variation of the argument induces a small variation of the value of the function.

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Convergent series

In mathematics, a series is the sum of the terms of an infinite sequence of numbers.

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Crelle's Journal

Crelle's Journal, or just Crelle, is the common name for a mathematics journal, the Journal für die reine und angewandte Mathematik (in English: Journal for Pure and Applied Mathematics).

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Dirichlet's test

In mathematics, Dirichlet's test is a method of testing for the convergence of a series. Abel's test and Dirichlet's test are convergence tests.

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Function (mathematics)

In mathematics, a function from a set to a set assigns to each element of exactly one element of.

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Improper integral

In mathematical analysis, an improper integral is an extension of the notion of a definite integral to cases that violate the usual assumptions for that kind of integral.

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Mathematics

Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.

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Niels Henrik Abel

Niels Henrik Abel (5 August 1802 – 6 April 1829) was a Norwegian mathematician who made pioneering contributions in a variety of fields.

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Power series

In mathematics, a power series (in one variable) is an infinite series of the form \sum_^\infty a_n \left(x - c\right)^n.

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Radius of convergence

In mathematics, the radius of convergence of a power series is the radius of the largest disk at the center of the series in which the series converges.

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Series (mathematics)

In mathematics, a series is, roughly speaking, the operation of adding infinitely many quantities, one after the other, to a given starting quantity.

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Summation by parts

In mathematics, summation by parts transforms the summation of products of sequences into other summations, often simplifying the computation or (especially) estimation of certain types of sums.

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