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...

variety of fields. His most famous single result is the first complete proof demonstrating the impossibility of solving the general quintic equation in radicals...

two groups referred to as the first and the second kind. A linear Volterra equation of the first kind is f ( t ) = ∫ a t K ( t , s ) x ( s ) d s {\displaystyle...

Friedrich Bessel who was the first to systematically study them in 1824, are canonical solutions y(x) of Bessel's differential equation x 2 d 2 y d x 2 + x...

functions Abel equation Abel equation of the first kind Abel–Goncharov interpolation Abel–Plana formula Abel function Abel's integral equation Abel's identity...

Monge–Ampère equation is a nonlinear second-order partial differential equation of special kind. A second-order equation for the unknown function u of two variables...

Systems Liénard equation at eqworld. Abel equation of the second kind at eqworld. Pilipenko A. M., and Biryukov V. N. «Investigation of Modern Numerical...

In mathematics, an algebraic equation or polynomial equation is an equation of the form P = 0 {\displaystyle P=0} , where P is a polynomial, usually with...

This equation is a special form of the more general weakly singular Volterra integral equation of the first kind, called Abel's integral equation: g (...

advised the young, aspiring Norwegian mathematician Niels Henrik Abel in a decisive way. Degen has received much of the credit for the introduction of more...

of S, pull back to a basis for the differentials of the first kind on S. Abel 1841. Appell & Goursat 1895, p. 248. Abel, Niels H. (1841). "Mémoire sur...

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 and n = 2 have been known since...

are two kinds of equations: identities and conditional equations. An identity is true for all values of the variables. A conditional equation is only...

"Construction of Exact Parametric or Closed Form Solutions of Some Unsolvable Classes of Nonlinear ODEs (Abel's Nonlinear ODEs of the First Kind and Relative...

exponential map through the corresponding Abel function X {\displaystyle {\mathcal {X}}} , satisfying the related Abel equation X ( exp ⁡ ( u ) ) = X (...

integral Differential of the first kind Jacobian variety Generalized Jacobian Moduli of algebraic curves Hurwitz's theorem on automorphisms of a curve Clifford's...

differential equations, determinants and number theory. Jacobi was born of Ashkenazi Jewish parentage in Potsdam on 10 December 1804. He was the second of four...

he were awarded the Abel Prize for their contributions to the field of partial differential equations. As a graduate student in the Princeton University...

Calculus and Fractional Differential Equations. New York: Wiley. pp. 1–2. ISBN 978-0-471-58884-9. Niels Henrik Abel (1823). "Oplösning af et Par Opgaver...

notion of flow is basic to the study of ordinary differential equations. Informally, a flow may be viewed as a continuous motion of points over time. More...

for several centuries. In 1824, Niels Henrik Abel proved the striking result that there are equations of degree 5 whose solutions cannot be expressed...

restricted to nonnegative values. The implicit function theorem provides conditions under which some kinds of implicit equations define implicit functions, namely...

found the first algebraic solutions to special cubic equations. Gerolamo Cardano used algebra to solve the cubic and quartic equation. Chapter 5: The Cunning...

the Hankel transform expresses any given function f(r) as the weighted sum of an infinite number of Bessel functions of the first kind Jν(kr). The Bessel...

and functional equation, and established a relation between its zeros and the distribution of prime numbers. This paper also contained the Riemann hypothesis...

but a list of various kinds of prime numbers (each with an accompanying table) List of zeta functions A differential equation is an equation involving...

quotated works that the Jacobi amplitude sine of the third part of the complete first kind integral K solves following quartic equation: ε 2 x 4 − 2 ε 2...

received other honours such as the 2016 Abel Prize. When announcing that Wiles had won the Abel Prize, the Norwegian Academy of Science and Letters described...

differential equations and integral equations into algebraic polynomial equations, and by simplifying convolution into multiplication. Once solved, the inverse...

This article records new taxa of fossil archosaurs of every kind that are scheduled described during the year 2025, as well as other significant discoveries...