Geodesic
Estimates of polynomials orthogonal with respect to the Legendre–Sobolev inner product
Matematičeskie zametki, Tome 62 (1997) no. 6, pp. 871-880 
F. Marcellan; B. P. Osilenker. Estimates of polynomials orthogonal with respect to the Legendre–Sobolev inner product. Matematičeskie zametki, Tome 62 (1997) no. 6, pp. 871-880. http://geodesic.mathdoc.fr/item/MZM_1997_62_6_a7/
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     author = {F. Marcellan and B. P. Osilenker},
     title = {Estimates of polynomials orthogonal with respect to the {Legendre{\textendash}Sobolev} inner product},
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     url = {http://geodesic.mathdoc.fr/item/MZM_1997_62_6_a7/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

For the Legendre–Sobolev orthonormal polynomials $\widehat B_n(x)=\widehat B_n(x;M,N)$ depending on the parameters $M\ge0$, $N\ge0$, weighted and uniform estimates on the orthogonality interval are obtained. It is shown that, unlike the Legendre orthonormal polynomials, the polynomials $\widehat B_n(x)$ for $M>0$, $N>0$ decay at the rate of $n^{-3/2}$ at the points 1 and -1. The values of $\widehat B'_n(\pm1)$ are calculated.

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