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24 de may. de 2024 · Legendre Polynomials are one of a set of classical orthogonal polynomials. These polynomials satisfy a second-order linear differential equation. This differential equation occurs naturally in the solution of initial boundary value problems in three dimensions which possess some spherical symmetry.
Hace 6 días · Legendre polynomials are eigenfunctions corresponding to eigenvalues λ = n ( n +1) of the singular Sturm--Liouville problem, (1 − x2)y ″ − 2xy. ′. + λy = 0, x ∈ ( − 1, 1), y( ± 1) < ∞, where n ∈ ℕ = {0, 1, 2, …} is a nonnegative integer. This equation can be written in a self-adjoint form.
26 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.
Hace 2 días · Legendre Series -- from Wolfram MathWorld. Calculus and Analysis. Series. Fourier Series.
Hace 5 días · The ordinary generating function for Legendre polynomials is \begin{equation} \label{EqLege1.1} G(x,t) = \frac{1}{\sqrt{1 -2xt + t^2}} = \sum_{n\ge 0} P_n (x)\, t^n , \end{equation} where P n ( x is the Legendre polynomial of degree n .
Hace 6 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.
24 de may. 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
