Bounds and Inequalities for Lm Extremal Polynomials
โ Scribed by Ying Guang Shi
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 150 KB
- Volume
- 115
- Category
- Article
- ISSN
- 0021-9045
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
The Christoffel functions for orthogonal polynomials are extended to the case of L m extremal polynomials with an even integer m and their properties are given.
In this paper, using the approach developed by the author in a previous paper, we deduce some bounds and inequalities for arbitrary orthogonal polynomials on finite intervals and give their various applications. 1995 Academic Press. Inc.
In this paper using a new effective approach we deduce some bounds and inequalities for general orthogonal polynomials on finite intervals and give their applications to convergence of orthogonal Fourier series, Lagrange interpolation, orthogonal series with gaps, and Hermite-Fejรฉr interpolation, as
The L m extremal polynomials in an explicit form with respect to the weights (1&x) &1ร2 (1+x) (m&1)ร2 and (1&x) (m&1)ร2 (1+x) &1ร2 for even m are given. Also, an explicit representation for the Cotes numbers of the corresponding Tura n quadrature formulas and their asymptotic behavior is provided. 1