March 1809. His parents were Claude-Joseph Liouville (an army officer) and Thérèse Liouville (née Balland). Liouville gained admission to the École Polytechnique...

Liouville's theorem has various meanings, all mathematical results named after Joseph Liouville: In complex analysis, see Liouville's theorem (complex...

In mathematics and its applications, a Sturm–Liouville problem is a second-order linear ordinary differential equation of the form: d d x [ p ( x ) d...

than any algebraic irrational number can be. In 1844, Joseph Liouville showed that all Liouville numbers are transcendental, thus establishing the existence...

In physics, Liouville's theorem, named after the French mathematician Joseph Liouville, is a key theorem in classical statistical and Hamiltonian mechanics...

In complex analysis, Liouville's theorem, named after Joseph Liouville (although the theorem was first proven by Cauchy in 1844), states that every bounded...

theorem is named after Joseph Liouville and Vladimir Arnold.: 270–272  The theorem was proven in its original form by Liouville in 1853 for functions on...

For Liouville's equation in Euclidean space, see Liouville–Bratu–Gelfand equation. In differential geometry, Liouville's equation, named after Joseph Liouville...

antiderivative of f of order α. The Riemann–Liouville integral is named for Bernhard Riemann and Joseph Liouville, the latter of whom was the first to consider...

In mathematics, Liouville's theorem, originally formulated by Joseph Liouville in 1833 to 1841, places an important restriction on antiderivatives that...

French mathematician Joseph Liouville. Jacobi's formula provides another representation of the same mathematical relationship. Liouville's formula is a generalization...

The Liouville lambda function, denoted by λ(n) and named after Joseph Liouville, is an important arithmetic function. Its value is +1 if n is the product...

introduced by Joseph Liouville in a series of papers from 1833 to 1841. An algebraic treatment of elementary functions was started by Joseph Fels Ritt in...

is complete require Galois theory). Galois' work was published by Joseph Liouville fourteen years after his death. The theory took longer to become popular...

we have the notion of integrability in the Liouville sense. (See the Liouville–Arnold theorem.) Liouville integrability means that there exists a regular...

book about Joseph Liouville without reaching any definitive conclusions. It is certainly possible that mathematicians (including Liouville) did not want...

For Liouville's equation in differential geometry, see Liouville's equation. In mathematics, Liouville–Bratu–Gelfand equation or Liouville's equation is...

mathematician Joseph Liouville. Euler–Liouville equation Liouville–Arnold theorem Liouville–Bratu–Gelfand equation Liouville–Green method Liouville's equation...

name of Joseph Catalan, in 1814. In 1825, he traveled to Paris and learned mathematics at École Polytechnique, where he met Joseph Liouville (1833). In...

Liouville is a small lunar impact crater that is located near the eastern limb of the Moon. It was named after French mathematician Joseph Liouville. It...

the mathematical field of differential geometry a Liouville surface (named after Joseph Liouville) is a type of surface which in local coordinates may...

Francesco Carlini in 1817, Joseph Liouville in 1837, George Green in 1837, Lord Rayleigh in 1912 and Richard Gans in 1915. Liouville and Green may be said...

differential Galois theory is due to Joseph Liouville in the 1830s and 1840s and hence referred to as Liouville's theorem. A standard example of an elementary...

transcendental. Joseph Liouville first proved the existence of transcendental numbers in 1844, and in 1851 gave the first decimal examples such as the Liouville constant...

the twentieth century, but almost a hundred years after his claim Joseph Liouville did manage to prove the existence of numbers that are not algebraic...

good here was refined by a number of mathematicians, starting with Joseph Liouville in 1844 and continuing with work of Axel Thue (1909), Carl Ludwig Siegel (1921)...

In mathematics, Liouville's theorem, proved by Joseph Liouville in 1850, is a rigidity theorem about conformal mappings in Euclidean space. It states...

Integrable systems Geometric integrability Frobenius integrability Foliation Liouville integrability In classical mechanics In quantum mechanics Quantum harmonic...

infinite sums. [example needed] Liouvillian functions were introduced by Joseph Liouville in a series of papers from 1833 to 1841. All elementary functions are...

Leibniz List of things named after Sophus Lie List of things named after Joseph Liouville List of things named after Andrey Markov List of things named after...