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DC Field | Value | Language |
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dc.contributor.author | Krasikov, I | - |
dc.date.accessioned | 2017-07-05T08:43:18Z | - |
dc.date.available | 2017-07-05T08:43:18Z | - |
dc.date.issued | 2017-07-12 | - |
dc.identifier.citation | Krasikov, I. (2017) 'On approximation of ultraspherical polynomials in the oscillatory region', Journal of Approximation Theory, 222, pp. 143-156. doi: 10.1016/j.jat.2017.07.003. | en_US |
dc.identifier.issn | 0021-9045 | - |
dc.identifier.uri | https://bura.brunel.ac.uk/handle/2438/14873 | - |
dc.description.abstract | For k 2 even, and −(2k + 1)/4, we provide a uniform approximation of the ultraspherical polynomials P( , ) k (x) in the oscillatory region with a very explicit error term. In fact, our result covers all for which the expression “oscillatory region” makes sense. To that end, we construct the almost equioscillating function g(x) = cpb(x) (1−x2)( +1)/2P( , ) k (x) = cos B(x) + r(x). Here the constant c = c(k, ) is defined by the normalization of P( , ) k (x), B(x) = R x 0 b(x)dx, and the functions b(x) and B(x), as well as bounds on the error term r(x), are given by some rather simple elementary functions. | en_US |
dc.language.iso | en | en_US |
dc.publisher | Elsevier | - |
dc.subject | orthogonal polynomials | en_US |
dc.subject | ultraspherical polynomials | en_US |
dc.subject | Gegenbauer polynomials | en_US |
dc.subject | uniform approximation | en_US |
dc.title | On approximation of ultraspherical polynomials in the oscillatory region | en_US |
dc.type | Article | en_US |
dc.identifier.doi | https://doi.org/10.1016/j.jat.2017.07.003 | - |
dc.relation.isPartOf | Journal of Approximation Theory | - |
pubs.publication-status | Published | - |
Appears in Collections: | Dept of Mechanical and Aerospace Engineering Research Papers |
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