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23 de abr. de 2024 · Legendre's equation comes up in many physical situations involving spherical symmetry. Legendre Polynomials. Legendre's polynomial can be defined explicitly: Pn(x) = 1 2n ⌊ n / 2 ⌋ ∑ k = 0 ( − 1)k(n k)(2n − 2k n)xn − 2k, where ⌊ · ⌋ is the floor function, and (n k) = n! k!(n − k)! = nk _ k! is the binomial coefficient.
Hace 4 días · The Legendre symbol is a function that encodes the information about whether a number is a quadratic residue modulo an odd prime. It is used in the law of quadratic reciprocity to simplify notation.
Hace 5 días · Legendre Identity -- from Wolfram MathWorld. Calculus and Analysis. Special Functions. Elliptic Integrals.
1 de may. 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.
29 de abr. de 2024 · TOPICS. Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics Foundations of Mathematics Geometry History and Terminology Number Theory Probability and Statistics Recreational Mathematics Topology Alphabetical Index New in MathWorld
Hace 5 días · Legendre's polynomials are orthogonal \begin{equation} \label{Eqlegendre.4} \int_{-1}^1 P_n (x) \, P_m (x) \,{\text d} x = \begin{cases} 0 , & \ \mbox{for} \quad n\ne m, \\ \frac{2}{2n+1} , & \ \mbox{for} \quad n = m. \end{cases} \end{equation}
5 de may. de 2024 · Introduction to Linear Algebra with Mathematica. Glossary. Preface. This section is devoted to expansions of real-valued functions into series over Laguerre polynomials. (7)f(x) =∑k≥0fkLk(x), fk =∫∞ 0 Lk. and Sonin polynomials. f(x) = ∑ k ≥ 0f ( α) k L ( α) k (x), f ( α) k = k! Γ(k + α + 1)∫∞0L ( α) k (x)e − xxαf(x)dx, k = 0, 1, 2, ….
