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On the Generating Function of Discrete Chebyshev Polynomials

Nikita Gogin, Mika Hirvensalo, On the Generating Function of Discrete Chebyshev Polynomials. TUCS Technical Reports 819, Turku Centre for Computer Science, 2007.

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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BibTeX entry:

@TECHREPORT{tGoHi07b,
  title = {On the Generating Function of Discrete Chebyshev Polynomials},
  author = {Gogin, Nikita and Hirvensalo, Mika},
  number = {819},
  series = {TUCS Technical Reports},
  publisher = {Turku Centre for Computer Science},
  year = {2007},
  keywords = {Orthogonal polynomials, Discrete Chebyshev polynomials, Krawtchouk polynomials, MacWilliams transform, Generating function, Heun equation},
  ISBN = {978-952-12-1896-5},
}

Belongs to TUCS Research Unit(s): FUNDIM, Fundamentals of Computing and Discrete Mathematics

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