Geodesic
Estimates of polynomials orthogonal with respect to the Legendre--Sobolev inner product
Matematičeskie zametki, Tome 62 (1997) no. 6, pp. 871-880

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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. 
@article{MZM_1997_62_6_a7,
     author = {F. Marcellan and B. P. Osilenker},
     title = {Estimates of polynomials orthogonal with respect to the {Legendre--Sobolev} inner product},
     journal = {Matemati\v{c}eskie zametki},
     pages = {871--880},
     publisher = {mathdoc},
     volume = {62},
     number = {6},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1997_62_6_a7/}
}
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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/