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Hace 3 días · These polynomial solutions are the Legendre polynomials, which we designate as \(y(x)=P_{n}(x)\). Furthermore, for \(n\) an even integer, \(P_{n}(x)\) is an even function and for \(n\) an odd integer, \(P_{n}(x)\) is an odd function.
Hace 5 días · Legendre Polynomials. 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 binomial coefficient.
Hace 3 días · Legendre Identity -- from Wolfram MathWorld. Calculus and Analysis. Special Functions. Elliptic Integrals.
Hace 4 días · This exact rule is known as the Gauss–Legendre quadrature rule. The quadrature rule will only be an accurate approximation to the integral above if f ( x ) is well-approximated by a polynomial of degree 2 n − 1 or less on [−1, 1] .
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20 de may. de 2024 · Legendre's Theorem. Let a , b and c be integers where any pair of the three are relatively prime. Moreover assume that at least one of ab , bc or ca is negative (i.e. they don't all have the same sign).
16 de may. de 2024 · See. Spherical Harmonic Addition Theorem. About MathWorld; MathWorld Classroom; Contribute; MathWorld Book; wolfram.com; 13,150 Entries
