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Nikita Gogin, Mika Hirvensalo:
On the Generating Function of Discrete Chebyshev Polynomials

ISBN: 978-952-12-1896-5

Techreport
Year: 2007
Month: Apr
Number: 819
Institution: TUCS
Keywords: Orthogonal polynomials, Discrete Chebyshev polynomials, Krawtchouk polynomials, MacWilliams transform, Generating function, Heun equation
Laboratory: Discrete Mathematics for Information Technology

Abstract

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 Heun differential equation, and that the closed form implies combinatorial identities that appear quite challenging to prove directly.


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