Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2024, Volume 235, Pages 34–39
DOI: https://doi.org/10.36535/2782-4438-2024-235-34-39 (Mi into1306) 		 
An approach to obtaining identities with binomial coefficients and orthogonal polynomials

V. A. Voblyi

All-Russian Institute for Scientific and Technical Information of Russian Academy of Sciences, Moscow
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DOI: https://doi.org/10.36535/2782-4438-2024-235-34-39
Abstract: A series of new combinatorial identities with binomial coefficients and orthogonal polynomials is obtained by using a unified approach. These identities contain Hermite polynomials, Legendre polynomials, Chebyshev polynomials of the first and second kind, Gegenbauer polynomials, and Krawtchouk polynomials.
Keywords: combinatorial identity, binomial coefficients, orthogonal polynomials, Hermite polynomials, Legendre polynomials, Chebyshev polynomials, Gegenbauer polynomials, Krawtchouk polynomials
Document Type: Article
UDC: 519.117, 517.587
MSC: 05A19, 33C45
Language: Russian
Citation: V. A. Voblyi, “An approach to obtaining identities with binomial coefficients and orthogonal polynomials”, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXV", Voronezh, April 26-30, 2024, Part 1, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 235, VINITI, Moscow, 2024, 34–39
Citation in format AMSBIB
\Bibitem{Vob24}
\by V.~A.~Voblyi
\paper An approach to obtaining identities with binomial coefficients and orthogonal polynomials
\inbook Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXV", Voronezh, April 26-30, 2024, Part 1
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2024
\vol 235
\pages 34--39
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into1306}
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