Geodesic
On a class of factors of the Chebyshev polynomials
Čebyševskij sbornik, Tome 22 (2021) no. 4, pp. 241-252

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The article defines a class of $D_n(x)$ polynomials by specially designed nodes. Each of $D_n(x)$ is the factor of the Chebyshev polynomial of the first kind $T_{2n}(x)$. The research task for polynomials $D_n(x)$ on the interval $[0,1]$ is reduced to find values $D_n(x)$. The article contains exact expressions and estimates of values $D_n(x)$ in special nodes.
Keywords: Chebyshev polynomials, Lobachevsky function, estimations. 
@article{CHEB_2021_22_4_a11,
     author = {S. Y. Soloviev},
     title = {On a class of factors of the {Chebyshev} polynomials},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {241--252},
     publisher = {mathdoc},
     volume = {22},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2021_22_4_a11/}
}
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S. Y. Soloviev. On a class of factors of the Chebyshev polynomials. Čebyševskij sbornik, Tome 22 (2021) no. 4, pp. 241-252. http://geodesic.mathdoc.fr/item/CHEB_2021_22_4_a11/