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Los polinomios de Legendre, igual que los de Hermite y Laguerre, son útiles en ramas de la Física y en el cálculo numérico ya que permiten el cómputo de integrales definidas sin necesidad de usar fórmulas analíticas, tan sólo fijando como intervalo de integración [ -1 ; +1] (con el correspondiente cambio de variable).
Adrien-Marie Legendre (born September 18, 1752, Paris, France—died January 10, 1833, Paris) was a French mathematician whose distinguished work on elliptic integrals provided basic analytic tools for mathematical physics. Little is known about Legendre’s early life except that his family wealth allowed him to study physics and mathematics ...
17 de abr. de 2022 · ルジャンドル多項式には、 漸化式 が成り立つ。. ルジャンドル多項式の定義と具体例と性質 (直交性・規格化・微分方程式・漸化式)について書かれています。. 各項目には丁寧な証明が付けられているので、よろしければご覧ください。.
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 ...
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.
The Legendre polynomials, sometimes called Legendre functions of the first kind, Legendre coefficients, or zonal harmonics (Whittaker and Watson 1990, p. 302), are solutions to the Legendre differential equation. If l is an integer, they are polynomials. The Legendre polynomials P_n(x) are illustrated above for x in ...
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 ...
