On a class of factors of the Chebyshev polynomials
https://doi.org/10.22405/2226-8383-2021-22-4-241-252
Abstract
The article defines a class of 𝐷𝑛(𝑥) polynomials by specially designed nodes. Each of 𝐷𝑛(𝑥) is the factor of the Chebyshev polynomial of the first kind 𝑇2𝑛(𝑥). The research task for
polynomials 𝐷𝑛(𝑥) on the interval [0,1] is reduced to find values 𝐷𝑛(𝑥). The article contains exact expressions and estimates of values 𝐷𝑛(𝑥) in special nodes.
About the Author
Sergey Yurievich Soloviev
Lomonosov Moscow State University
Russian Federation
Russian Federation
doctor of physical and mathematical sciences, professor
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Review
For citations:
Soloviev S.Yu. On a class of factors of the Chebyshev polynomials. Chebyshevskii Sbornik. 2021;22(4):241-252. (In Russ.) https://doi.org/10.22405/2226-8383-2021-22-4-241-252
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