Liouville

Phrases with the word

Liouville's formula Abel-Jacobi-Liouville identity Liouville's equation Liouville's theorem

Examples

Along with the above remarks about measure, it shows that the set of Liouville numbers and its complement decompose the reals into two sets, one of which is meagre, and the other of Lebesgue measure zero. Source: Internet

A Liouville number is irrational but does not have this property, so it can't be algebraic and must be transcendental. Source: Internet

All Liouville numbers are transcendental, but not vice versa. Source: Internet

For example, Liouville showed that is at most 53. Hardy and Littlewood showed that all sufficiently large numbers are the sum of at most 19 fourth powers. Source: Internet

Here are a few examples: Dirichlet convolutions : where λ is the Liouville function. Source: Internet

Elementary functions were introduced by Joseph Liouville in a series of papers from 1833 to 1841. Source: Internet