Geodesic
An approach to obtaining identities with binomial coefficients and orthogonal polynomials
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, 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, Tome 235 (2024), pp. 34-39.

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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, Hermite polynomials, Chebyshev polynomials, Gegenbauer polynomials
Mots-clés : binomial coefficients, orthogonal polynomials, Legendre polynomials, Krawtchouk polynomials 
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V. A. Voblyi. An approach to obtaining identities with binomial coefficients and orthogonal polynomials. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, 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, Tome 235 (2024), pp. 34-39. http://geodesic.mathdoc.fr/item/INTO_2024_235_a2/

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