Chebyshev approximations for \(\cos \pi x^ 2\) and \(\sin \pi x^ 2\) with applications (Q582802)
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scientific article; zbMATH DE number 4131520
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Chebyshev approximations for \(\cos \pi x^ 2\) and \(\sin \pi x^ 2\) with applications |
scientific article; zbMATH DE number 4131520 |
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Chebyshev approximations for \(\cos \pi x^ 2\) and \(\sin \pi x^ 2\) with applications (English)
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1990
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The author, by using certain identities for the Chebyshev polynomials \(T_ r(x^ 2)\), derives an expansion for cos (\(\pi\) \(x^ 2/2)\) of the form \(\cos (\pi x^ 2/2)=\sum '\beta_{2r}T_{2r}(x).\) A similar expansion is obtained for sin (\(\pi\) \(x^ 2/2)\). Application to the evaluation of Fresnel integrals is given.
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Chebyshev polynomials
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Fresnel integrals
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