On the Generating Function of Discrete Chebyshev Polynomials

We give a closed form for the generating function of the discrete Chebyshev polynomials. It is 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,...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2017-07, Vol.224 (2), p.250-257
Main Authors: Gogin, N., Hirvensalo, M.
Format: Article
Language:English
Subjects:
Chebyshev approximation
Combinatorial analysis
Differential equations
Exact solutions
Mathematical analysis
Mathematics
Mathematics and Statistics
Polynomials
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Summary:We give a closed form for the generating function of the discrete Chebyshev polynomials. It is 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 it implies combinatorial identities that appear quite challenging to prove directly.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-017-3410-8