Abstract
Given numbers \({n,s \in \mathbb{N}}\), \({n \geq 2}\), and the \({n}\)th-degree monic Chebyshev polynomial of the first kind \({\widehat T_n(x)}\), the polynomial system “induced” by \({\widehat T_n(x)}\) is the system of orthogonal polynomials \({\{p_{k}^{n,s} \}}\) corresponding to the modified measure \({d \sigma^{n,s}(x)=\widehat T^{2s}_n(x) d\sigma(x)}\), where \({d\sigma(x)=1/\sqrt{1-x^{2}}dx}\) is the Chebyshev measure of the first kind. Here we are concerned with the problem of determining the coefficients in the three-term recurrence relation for the polynomials \({p^{n,s}_{k}}\). The desired coefficients are obtained analytically in a closed form.
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The work was supported in part by the Serbian Ministry of Education, Science and Technological Development.
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Cvetković, A.S., Matejić, M.M. & Milovanović, G.V. Orthogonal Polynomials for Modified Chebyshev Measure of the First Kind. Results. Math. 69, 443–455 (2016). https://doi.org/10.1007/s00025-016-0529-8
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DOI: https://doi.org/10.1007/s00025-016-0529-8