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This article is cited in 9 scientific papers (total in 9 papers)
Estimates of polynomials orthogonal with respect to the Legendre–Sobolev inner product
F. Marcellana, B. P. Osilenkerb a Carlos III University of Madrid
b Moscow State University of Civil Engineering
Abstract:
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.
Received: 02.04.1996
Citation:
F. Marcellan, B. P. Osilenker, “Estimates of polynomials orthogonal with respect to the Legendre–Sobolev inner product”, Mat. Zametki, 62:6 (1997), 871–880; Math. Notes, 62:6 (1997), 731–738
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https://www.mathnet.ru/eng/mzm1676https://doi.org/10.4213/mzm1676 https://www.mathnet.ru/eng/mzm/v62/i6/p871
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