Geodesic
On the generating function of discrete Chebyshev polynomials
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXVII, Tome 448 (2016), pp. 124-134 
N. Gogin; M. Hirvensalo. On the generating function of discrete Chebyshev polynomials. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXVII, Tome 448 (2016), pp. 124-134. http://geodesic.mathdoc.fr/item/ZNSL_2016_448_a7/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We give a closed form for the generating function of the discrete Chebyshev polynomials. The closed form consists of the MacWilliams transform of Jacobi polynomials together with a binomial multiplicative factor. It turns out that the desired closed form is a solution to a special case of the Heun differential equation, and that the closed form implies combinatorial identities that appear quite challenging to prove directly.

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