This is the list of things named after

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. His most famous single result is the first complete proof demonstrating the impossibility of solvin ...

(1802–1829), a Norwegian mathematician.

Mathematics

* Abel's binomial theorem *

Abel elliptic functions In mathematics Abel elliptic functions are a special kind of elliptic functions, that were established by the Norwegian mathematician Niels Henrik Abel. He published his paper "Recherches sur les Fonctions elliptiques" in Crelle's Journal in 1827. ...

Abel equation The Abel equation, named after Niels Henrik Abel, is a type of functional equation of the form :f(h(x)) = h(x + 1) or :\alpha(f(x)) = \alpha(x)+1. The forms are equivalent when is invertible. or control the iteration of . Equivalence The seco ...

Abel equation of the first kind In mathematics, an Abel equation of the first kind, named after Niels Henrik Abel, is any ordinary differential equation that is cubic in the unknown function. In other words, it is an equation of the form :y'=f_3(x)y^3+f_2(x)y^2+f_1(x)y+f_0(x) ...

* Abel–Goncharov interpolation *

Abel–Plana formula In mathematics, the Abel–Plana formula is a summation formula discovered independently by and . It states that :\sum_^\infty f(n)=\frac 1 2 f(0)+ \int_0^\infty f(x) \, dx+ i \int_0^\infty \frac \, dt. It holds for functions ''f'' that are hol ...

Abel function The Abel equation, named after Niels Henrik Abel, is a type of functional equation of the form :f(h(x)) = h(x + 1) or :\alpha(f(x)) = \alpha(x)+1. The forms are equivalent when is invertible. or control the iteration of . Equivalence The se ...

* Abel's integral equation *

Abel's identity In mathematics, Abel's identity (also called Abel's formula or Abel's differential equation identity) is an equation that expresses the Wronskian of two solutions of a homogeneous second-order linear ordinary differential equation in terms of a c ...

* Abel's inequality *

Abel's irreducibility theorem In mathematics, Abel's irreducibility theorem, a field theory result described in 1829 by Niels Henrik Abel, asserts that if ''ƒ''(''x'') is a polynomial over a field ''F'' that shares a root with a polynomial ''g''(''x'') that is irreduci ...

Abel–Jacobi map In mathematics, the Abel–Jacobi map is a construction of algebraic geometry which relates an algebraic curve to its Jacobian variety. In Riemannian geometry, it is a more general construction mapping a manifold to its Jacobi torus. The name der ...

** Abel–Jacobi theorem * Abel polynomials *

Abel's summation formula In mathematics, Abel's summation formula, introduced by Niels Henrik Abel, is intensively used in analytic number theory and the study of special functions to compute series. Formula Let (a_n)_^\infty be a sequence of real or complex numbers. ...

** Abelian means *

Abel's test In mathematics, Abel's test (also known as Abel's criterion) is a method of testing for the convergence of an infinite series. The test is named after mathematician Niels Henrik Abel. There are two slightly different versions of Abel's test &nd ...

Abel's theorem In mathematics, Abel's theorem for power series relates a limit of a power series to the sum of its coefficients. It is named after Norwegian mathematician Niels Henrik Abel. Theorem Let the Taylor series G (x) = \sum_^\infty a_k x^k be a pow ...

Abelian theorem In mathematics, Abelian and Tauberian theorems are theorems giving conditions for two methods of summing divergent series to give the same result, named after Niels Henrik Abel and Alfred Tauber. The original examples are Abel's theorem showing th ...

Abel–Ruffini theorem In mathematics, the Abel–Ruffini theorem (also known as Abel's impossibility theorem) states that there is no solution in radicals to general polynomial equations of degree five or higher with arbitrary coefficients. Here, ''general'' means th ...

Abel transform In mathematics, the Abel transform,N. H. Abel, Journal für die reine und angewandte Mathematik, 1, pp. 153–157 (1826). named for Niels Henrik Abel, is an integral transform often used in the analysis of spherically symmetric or axially symme ...

* Abel transformation *

Abelian category In mathematics, an abelian category is a category in which morphisms and objects can be added and in which kernels and cokernels exist and have desirable properties. The motivating prototypical example of an abelian category is the category of ...

** Pre-abelian category ** Quasi-abelian category *

Abelian group In mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written. That is, the group operation is comm ...

Abelianization In mathematics, more specifically in abstract algebra, the commutator subgroup or derived subgroup of a group is the subgroup generated by all the commutators of the group. The commutator subgroup is important because it is the smallest normal ...

** Metabelian group **

Non-abelian group In mathematics, and specifically in group theory, a non-abelian group, sometimes called a non-commutative group, is a group (''G'', ∗) in which there exists at least one pair of elements ''a'' and ''b'' of ''G'', such that ''a'' ∗ ' ...

Abelian extension In abstract algebra, an abelian extension is a Galois extension whose Galois group is abelian. When the Galois group is also cyclic, the extension is also called a cyclic extension. Going in the other direction, a Galois extension is called solvable ...

Abelian integral In mathematics, an abelian integral, named after the Norwegian mathematician Niels Henrik Abel, is an integral in the complex plane of the form :\int_^z R(x,w) \, dx, where R(x,w) is an arbitrary rational function of the two variables x and w, wh ...

Abelian surface In mathematics, an abelian surface is a 2-dimensional abelian variety. One-dimensional complex tori are just elliptic curves and are all algebraic, but Riemann discovered that most complex tori of dimension 2 are not algebraic via the Riemann bi ...

* Abelian variety **

Abelian variety of CM-type In mathematics, an abelian variety ''A'' defined over a field ''K'' is said to have CM-type if it has a large enough commutative subring in its endomorphism ring End(''A''). The terminology here is from complex multiplication theory, which was deve ...

** Dual abelian variety *

Abelian von Neumann algebra In functional analysis, an abelian von Neumann algebra is a von Neumann algebra of operators on a Hilbert space in which all elements commute. The prototypical example of an abelian von Neumann algebra is the algebra ''L''∞(''X'', μ) for μ a ...

Geography

* Abeltoppen, a mountain in Dickson Land at Spitsbergen, Svalbard. * , a street in the 12th arrondissement of

Paris Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), ma ...

in front of the

Gare de Lyon The Gare de Lyon, officially Paris-Gare-de-Lyon, is one of the six large mainline railway stations in Paris, France. It handles about 148.1 million passengers annually according to the estimates of the SNCF in 2018, with SNCF railways and RER ...

mainline station.

Other

Abel Abel ''Hábel''; ar, هابيل, Hābīl is a Biblical figure in the Book of Genesis within Abrahamic religions. He was the younger brother of Cain, and the younger son of Adam and Eve, the first couple in Biblical history. He was a shepherd ...

, a

lunar Lunar most commonly means "of or relating to the Moon". Lunar may also refer to: Arts and entertainment * ''Lunar'' (series), a series of video games * "Lunar" (song), by David Guetta * "Lunar", a song by Priestess from the 2009 album ''Prior t ...

crater. * Abel Prize

References

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Niels Henrik Abel