Mathematician:Adrien-Marie Legendre

Mathematician
French mathematician, focusing in the fields of statistics, abstract algebra, number theory and analysis.

His work formed the basis for work by many others, including and.

Gave an early proof of Fermat's Last Theorem for $n = 5$.

Attempted a proof of the Law of Quadratic Reciprocity in $1785$, but it was flawed. It was eventually proven by in $1798$. Pioneered work on the distribution of primes and its application to number theory.

Conjectured that $\map \pi n$ approaches $\dfrac n {\map \ln n - 1 \cdotp 08366}$ as $n \to \infty$, which is very close to correct. In this context, $1 \cdotp 08366$ is known as Legendre's constant.

Known for the Legendre Transform, which is commonly used to go from the Lagrangian to the Hamiltonian Function in Classical Mechanics.

Developed the Least Squares Method for linear regression.

Investigated the Diophantine Equation $a x^2 + b y^2 + c z^2 = 0$ which is known as the Legendre Equation.

Introduced the notation $\map \Gamma z$ as the Gamma function.

Has a moon crater named after him.

Nationality
French

History

 * Born: 18 Sept 1752, Paris (or possibly Toulouse), France
 * Died: 10 Jan 1833, Paris, France

Theorems and Definitions

 * Associated Legendre Function
 * Legendre's Constant
 * Legendre's Differential Equation
 * Legendre Polynomial
 * Legendre Symbol
 * Legendre Transform


 * Legendre's Conjecture
 * Legendre's Duplication Formula
 * Legendre Equation
 * Legendre's Formula (also known as De Polignac's Formula for )
 * Legendre's Theorem


 * Saccheri-Legendre Theorem (with )


 * Factorial Divisible by Prime Power

Publications

 * 1782: Recherches sur la trajectoire des projectiles dans les milieux résistants
 * 1784: Recherches sur la figure des planètes which contains the Legendre polynomials
 * 1785: Recherches d'analyse indéterminée
 * 1787: Mémoire sur les opérations trigonométriques dont les résultats dépendent de la figure de la terre
 * 1794: Éléments de Géométrie, a reorganization of with simpler but just as rigorous proofs.
 * 1798: Essai sur la Théorie des Nombres, 2 volumes, possibly the first treatise dedicated solely to number theory.
 * 1808: Théorie des Nombres, a second edition of Essai sur la Théorie des Nombres
 * 1811: Exercices du Calcul Intégral, Volume 1
 * 1817: Exercices du Calcul Intégral, Volume 2
 * 1819: Exercices du Calcul Intégral, Volume 3
 * 1825: Traité des Fonctions Elliptiques, Volume 1
 * 1826: Traité des Fonctions Elliptiques, Volume 2
 * 1830: Traité des Fonctions Elliptiques, Volume 3
 * 1830: Théorie des Nombres, an expanded version of Essai sur la Théorie des Nombres, including work from the intervening years

Also known as
Some sources leave the name unhyphenated: Adrien Marie Legendre.