The Abel equation, named after Niels Henrik Abel, is a type of functional equation of the form f ( h ( x ) ) = h ( x + 1 ) {\displaystyle f(h(x))=h(x+1)}...

and Abel had studied all the latest mathematical literature in the university library. During that time, Abel started working on the quintic equation in...

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...

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...

{\displaystyle f(h(x))=h(x+1)\,\!} (Abel equation) f ( h ( x ) ) = c f ( x ) {\displaystyle f(h(x))=cf(x)\,\!} (Schröder's equation). f ( h ( x ) ) = ( f ( x )...

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...

Tartaglia to equations of degree 3 and that of Lodovico Ferrari for equations of degree 4. Finally Niels Henrik Abel proved, in 1824, that equations of degree...

starting height, find an equation of the curve that yields this result. The tautochrone problem is a special case of Abel's mechanical problem when T...

order differential equation: v d v d x + f ( x ) v + g ( x ) = 0 {\displaystyle v{dv \over dx}+f(x)v+g(x)=0} which is an Abel equation of the second kind...

(second-degree) and quartic (fourth-degree) equations, but not for higher-degree equations, by the Abel–Ruffini theorem.) trigonometrically numerical...

this relation is called the translation functional equation, cf. Schröder's equation and Abel equation. On a logarithmic scale, this reduces to the nesting...

mathematical function Schröder's equation – Equation for fixed point of functional composition Abel equation – Equation for function that computes iterated...

Anosov flows are isomorphic to Bernoulli shifts. Abel equation Iterated function Schröder's equation Infinite compositions of analytic functions D.V....

Schröder's equation to the older Abel equation, α(h(x)) = α(x) + 1. Similarly, the change of variables Ψ(x) = log(φ(x)) converts Schröder's equation to Böttcher's...

an equation is a mathematical formula that expresses the equality of two expressions, by connecting them with the equals sign =. The word equation and...

Frederick Abel, worked to improve the properties of gunpowder during the late 19th century. This formed the basis for the Noble-Abel gas equation for internal...

Wayback Machine.) Iterated function Function composition Abel equation Schröder's equation Flow (mathematics) Superfunction Fractional calculus Half-exponential...

roots, cube roots, etc)? The Abel–Ruffini theorem provides a counterexample proving that there are polynomial equations for which such a formula cannot...

interpolation Abel–Plana formula Abel function Abel's integral equation Abel's identity Abel's inequality Abel's irreducibility theorem Abel–Jacobi map Abel–Jacobi...

texts) states that no three positive integers a, b, and c satisfy the equation an + bn = cn for any integer value of n greater than 2. The cases n = 1...

of Schröder's equation, for his proof, Kneser had constructed the "superfunction" of the exponential map through the corresponding Abel function X {\displaystyle...

algebra, the theory of equations is the study of algebraic equations (also called "polynomial equations"), which are equations defined by a polynomial...

mathematics, Liouville's formula, also known as the Abel–Jacobi–Liouville identity, is an equation that expresses the determinant of a square-matrix solution...

The Abel Prize (/ˈɑːbəl/ AH-bəl; Norwegian: Abelprisen [ˈɑ̀ːbl̩ˌpriːsn̩]) is awarded annually by the King of Norway to one or more outstanding mathematicians...

in 1983 by Data I/O Corporation, in Redmond, Washington. ABEL includes both concurrent equation and truth table logic formats as well as a sequential state...

mathematics, a quartic equation is one which can be expressed as a quartic function equaling zero. The general form of a quartic equation is a x 4 + b x 3 +...

the regularity of the Monge–Ampère equation, with the former winning the Fields Medal in 2018 and the latter the Abel Prize in 2023. Given two independent...

In physics, the Hamilton–Jacobi equation, named after William Rowan Hamilton and Carl Gustav Jacob Jacobi, is an alternative formulation of classical mechanics...

quartic equations were solved, until the first half of the 19th century, when the impossibility of such a general solution was proved with the Abel–Ruffini...

differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the...