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Hace 3 días · Adrien-Marie Legendre. The Legendre equation is the second order differential equation with a real parameter λ. \ [ \left ( 1-x^2\right) y'' -2x\,y' + \lambda\, y =0 , \qquad -1 < x < 1 . \] This equation has two regular singular points x = ±1 where the leading coefficient (1 − x ²) vanishes.
Hace 4 días · Eq.\eqref{Eqlegendre.1} is named after a French mathematician Adrien-Marie Legendre (1752--1833) who introduced the Legendre polynomials in 1782. Legendre's equation comes up in many physical situations involving spherical symmetry.
25 de jun. de 2024 · The final 18th-century contribution to the theory of parallels was Adrien-Marie Legendre’s textbook Éléments de géométrie (Elements of Geometry and Trigonometry), the first edition of which appeared in 1794. Legendre presented an elegant demonstration that purported to show that the sum of the angles of a triangle is equal to two right ...
29 de jun. de 2024 · In mathematics, the Legendre transformation (or Legendre transform), first introduced by Adrien-Marie Legendre in 1787 when studying the minimal surface problem, is an involutive transformation on real-valued functions that are convex on a real variable. Specifically, if a real-valued multivariable function is convex on one of its independent ...
Hace 5 días · A glance at Paulo Ribenboim's Fermat's Last Theorem for amateurs, Franz Lemmermeyer's Reciprocity Laws and L.E. Dickson's History of the Theory of Numbers, reveals the existence of many past number theorists about whom little is known.
23 de jun. de 2024 · Sophie Germain, French mathematician who contributed notably to the study of acoustics, elasticity, and the theory of numbers. She proved several special cases of Fermat’s last theorem, and her method provided the basis of Legendre’s proof for n = 5.
Hace 1 día · The method was published first by Adrien-Marie Legendre in 1805, but Gauss claimed in Theoria motus (1809) that he had been using it since 1794 or 1795. In the history of statistics, this disagreement is called the "priority dispute over the discovery of the method of least squares".
