Abstract
The paper lists a number of problems that motivate consideration of special linear combinations of polynomials, orthogonal with the weight p(x) on the interval (a,b). We study properties of the polynomials, as well as the necessary and sufficient conditions for their orthogonality. The special linear combinations of Chebyshev orthogonal polynomials of four kinds with absolutely constant coefficients hold a distinguished place in the class of such linear combinations.
| Original language | English |
|---|---|
| Pages (from-to) | 1-18 |
| Number of pages | 18 |
| Journal | Journal of Mathematical Analysis and Applications |
| Volume | 299 |
| Issue number | 1 |
| DOIs | |
| State | Published - 1 Nov 2004 |
Keywords
- Bernstein-Szegö polynomials
- Chebyshev polynomials
- Extrema properties
- Linear combinations
- Linearization coefficients
- Orthogonal polynomials
- Weight function