Geodesic
Estimates of polynomials orthogonal with respect to the Legendre–Sobolev inner product
Matematičeskie zametki, Tome 62 (1997) no. 6, pp. 871-880 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     title = {Estimates of polynomials orthogonal with respect to the {Legendre{\textendash}Sobolev} inner product},
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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/

[1] Bavinck H., Meijer H. G., “Orthogonal polynomials with respect to a symmetric inner product involving derivatives”, Appl. Anal., 33 (1992), 103–117 | DOI | MR

[2] Bavinck H., Meijer H. G., “On orthogonal polynomials with respect to an inner product involving derivatives: zeros and recurrence relations”, Indag. Math. (N.S.), 1 (1990), 7–18 | DOI | MR

[3] Alfaro M., Marcellan F., Meijer H. G., Rezola M. L., “Symmetric orthogonal polynomials for Sobolev-type inner products”, J. Math. Anal., 184 (1989), 360–381 | DOI | MR

[4] Evans W. D., Littlejohn L. L., Marcellan F., Markett C., Ronveaux A., “On recurrence relations for Sobolev orthogonal polynomials”, SIAM J. Math. Anal., 26 (1995), 446–467 | DOI | MR | Zbl

[5] Alfaro M., Marcellan F., Rezola M. L., Ronveaux A., “On orthogonal polynomials of Sobolev type: algebraic properties and zeros”, SIAM J. Math. Anal., 23 (1992), 737–757 | DOI | MR | Zbl

[6] Marcellan F., Alfaro M., Rezola M. L., “Orthogonal polynomials on Sobolev spaces: old and new results”, J. Comput. Appl. Math., 48 (1993), 113–132 | DOI | MR

[7] Suetin P. K., Klassicheskie ortogonalnye mnogochleny, Nauka, M., 1979 | Zbl

[8] Guadalupe J. J., Perez M., Varona J. L., “Asymptotic behaviour of orthogonal polynomials relative to measures with mass points”, Mathematika, 40 (1993), 331–334 | MR

[9] Rafalson S. Z., “O polinomakh, ortogonalnykh s nagruzkoi”, Izv. vuzov. Matem., 1965, no. 3, 146–154 | MR

[10] Sege G., Ortogonalnye mnogochleny, GIFML, M., 1962