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- W2950476959 abstract "For $k ge 2$ even, and $ alpha ge -(2k+1)/4 $, we provide a uniform approximation of the ultraspherical polynomials $ P_k^{(alpha,, alpha)}(x) $ in the with a very explicit error term. In fact, our result covers all $alpha$ for which the expression oscillatory region makes sense. We show that there the function $g(x)={c sqrt{b(x)} , (1-x^2)^{(alpha+1)/2} P_k^{(alpha, alpha)}(x)=cos mathcal{B}(x)+ r(x)}$, where $c=c(k, alpha)$ is defined by the normalization, $mathcal{B}(x)=int_{0}^ x b(x) dx$, and the functions $c,, b(x), , mathcal{B}(x)$, as well as bounds on the error term $r(x)$ are given by some rather simple elementary functions." @default.
- W2950476959 created "2019-06-27" @default.
- W2950476959 creator A5044693535 @default.
- W2950476959 date "2016-08-29" @default.
- W2950476959 modified "2023-09-27" @default.
- W2950476959 title "On approximation of ultraspherical polynomials in the oscillatory region" @default.
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- W2950476959 hasPublicationYear "2016" @default.
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