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What are Legendre Polynomials and how are they related to differential equations? Learn about their definition, properties, applications, and examples in this chapter of the Mathematics LibreTexts book on A First Course in Differential Equations for Scientists and Engineers. Compare them with other special functions in the second course book.
Gauss was correct, but one could understand how hurtful Legendre must have found an attack on the rigour of his results by such a young man. Of course Gauss did not state that he was improving Legendre's result but rather claimed the result for himself since his was the first completely rigorous proof. Legendre later wrote (see [20]):- This excessive impudence is unbelievable in a man who has ...
The Legendre Group is a family-owned, independent company founded in 1946 which has become a major player in the construction, real estate and energy sectors of the future. Promoting innovation and long-term vision, the Legendre Group is diversifying its activities and extending its geographical coverage nationally and internationally from its ...
ルジャンドル多項式（ルジャンドルたこうしき、英: Legendre polynomial ）とは、ルジャンドルの微分方程式を満たすルジャンドル関数のうち次数が非負整数のものを言う。 直交多項式の一種である。
The first property that the Legendre polynomials have is the Rodrigues formula: Pn(x) = 1 2nn! dn dxn(x2 − 1)n, n ∈ N0. From the Rodrigues formula, one can show that Pn(x) is an n th degree polynomial. Also, for n odd, the polynomial is an odd function and for n even, the polynomial is an even function.
勒让德多项式是描述矩形表面和口径的另外一组 多项式 集合，它的优点是具有正交性。. 由于存在正交性条件，高阶项系数趋于零，并且增加和删除一个项对其他项没有影响。. 不过，这个多项式集合通常不在光学设计软件中使用。. [1] 中文名. 勒让德多项式 ...
Adrien-Marie Legendre (París, 1752 - Auteuil, Francia, 1833) Matemático francés. Tras completar sus estudios en el Collège Mazarin, obtuvo una cátedra de matemáticas en la Escuela Militar de París, en la que ejerció la docencia (1775-1780) y para la que completó un estudio sobre la trayectoria de los proyectiles que le supuso el Premio de la Academia de Berlín en 1782.
