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24 de jun. de 2024 · Adrien-Marie Legendre. The Legendre equation is the second order differential equation with a real parameter λ. (1 − x2)y ″ − 2xy. + λy = 0, − 1 < x < 1. This equation has two regular singular points x = ±1 where the leading coefficient (1 − x ²) vanishes.
25 de jun. de 2024 · Based on the tables by Anton Felkel and Jurij Vega, Adrien-Marie Legendre conjectured in 1797 or 1798 that π(a) is approximated by the function a / (A log a + B), where A and B are unspecified constants. In the second edition of his book on number theory (1808) he then made a more precise conjecture, with A = 1 and B = −1.08366.
Hace 3 días · 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.
Hace 6 días · In 1783, in a paper sent to the Académie, Adrien-Marie Legendre had introduced what are now known as associated Legendre functions. If two points in a plane have polar coordinates ( r , θ) and ( r ', θ'), where r ' ≥ r , then, by elementary manipulation, the reciprocal of the distance between the points, d , can be written as:
15 de jun. de 2024 · 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 ...
25 de jun. de 2024 · In 1798, Adrien-Marie Legendre first guessed this theorem. This was from his study on primes under 1,000,000. Then, in 1896, Jacques-Salomon Hadamard and Charles de la Vallée Poussin proved it. They used complex math, including the Riemann zeta function.
