Weighted integration of periodic functions on the real line. (Q1855679)
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scientific article; zbMATH DE number 1861077
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Weighted integration of periodic functions on the real line. |
scientific article; zbMATH DE number 1861077 |
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Weighted integration of periodic functions on the real line. (English)
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28 January 2003
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Integration of periodic functions on the real line with an even rational weight function is considered. A transformation method of such integrals to the integrals on \((-1,1)\) with respect to the Szegő-Bernstein weights and a construction of the corresponding Gaussian quadrature formulas are given. The recursion coefficients in the three-term recurrence relation for the corresponding orthogonal polynomials are obtained in an analytic form. Numerical examples are also included.
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Gauss type quadratures
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error term
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convergence
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orthogonal polynomials
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nonnegative measure
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weights
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Chebyshev weight
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Szegő-Bernstein weights
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nodes
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modified moments
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Chebyshev polynomials
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periodic functions
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three-term recurrence relation
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numerical examples
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