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22 de jun. 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
24 de jun. de 2024 · The eigenfunction corresponding to eigenvalues λ n = n ( n +1), n = 0, 1, 2, …, are convensionally called associated Legendre functions. They usually are denoted by Pmn(x), m = 0, 1, 2, …, n; or by Pn ( m, x ). The function Pn ( m, x) is a polynomial of degree n if and only if m is even.
Hace 6 días · In trigonometry, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined. Geometrically, these are identities involving certain functions of one or more angles. They are distinct from triangle identities ...
15 de jun. de 2024 · Legendre's polynomial can be defined explicitly: Pn(x) = 1 2n ∑k=0⌊n/2⌋ (−1)k(n k)(2n − 2k n)xn−2k, (2) (2) P n ( x) = 1 2 n ∑ k = 0 ⌊ n / 2 ⌋ ( − 1) k ( n k) ( 2 n − 2 k n) x n − 2 k, where ⌊ · ⌋ is the floor function, and (n k) = n! k!(n − k)! = nk−− k! ( n k) = n! k! ( n − k)! = n k _ k! is the ...
20 de jun. de 2024 · 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}
25 de jun. 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
22 de jun. de 2024 · LegendreP -- from Wolfram MathWorld. History and Terminology. Wolfram Language Commands.
