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http://bura.brunel.ac.uk/handle/2438/14873
Title: | On approximation of ultraspherical polynomials in the oscillatory region |
Authors: | Krasikov, I |
Keywords: | orthogonal polynomials;ultraspherical polynomials;Gegenbauer polynomials;uniform approximation |
Issue Date: | 12-Jul-2017 |
Publisher: | Elsevier |
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. |
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. |
URI: | https://bura.brunel.ac.uk/handle/2438/14873 |
DOI: | https://doi.org/10.1016/j.jat.2017.07.003 |
ISSN: | 0021-9045 |
Appears in Collections: | Dept of Mechanical and Aerospace Engineering Research Papers |
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