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Results tagged with legendre-polynomials
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user 89429
2
votes
Legendre Polynomial Integral
The integral can be evaluate from the formula which express the product of two Legendre polynomials as a sum of Legendre polynomials (proved by F. Neumann and J.C. Adams, 1878), see e.g. the paper of …
- 4,034
2
votes
Accepted
Bounds on Legendre polynomials on the complex plane
Setting $Q_{n}(z)=(n+1/2)^{1/2}P_{n}(z)$ for the orthonormalized Legendre polynomial, and
$$\kappa_{n}(z)=\sum_{j=0}^{n}|Q_{j}(z)|^{2},$$
for the inverse of the Christoffel function, it is known that …
- 4,034
10
votes
Recurrence of Legendre polynomial roots/ quadrature points
It is a conjecture of Stieltjes, apparently still open, see
T.J. Stieltjes, Letter No. 275 of Oct. 2, 1890, in Correspondance d'Hermite et de
Stieltjes, vol 2, Gauthier-Villars, Paris, 1905.
that Le …
- 4,034