Integral formulas for Chebyshev polynomials and the error term of interpolatory quadrature formulae for analytic functions
| Autor: | Sotirios E. Notaris |
|---|---|
| Rok vydání: | 2006 |
| Předmět: |
Chebyshev polynomials
Pure mathematics Algebra and Number Theory Applied Mathematics Mathematical analysis Chebyshev iteration Chebyshev's sum inequality Chebyshev filter Mathematics::Numerical Analysis Computational Mathematics Chebyshev pseudospectral method Chebyshev equation Clenshaw–Curtis quadrature Analytic function Mathematics |
| Zdroj: | Mathematics of Computation. 75:1217-1232 |
| ISSN: | 0025-5718 |
| DOI: | 10.1090/s0025-5718-06-01859-x |
| Popis: | We evaluate explicitly the integrals ∫ 1 -1 π n (t)/(r t)dt, |r| ≠ 1, with the π n being any one of the four Chebyshev polynomials of degree n. These integrals are subsequently used in order to obtain error bounds for interpolatory quadrature formulae with Chebyshev abscissae, when the function to be integrated is analytic in a domain containing [-1,1] in its interior. |
| Databáze: | OpenAIRE |
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