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Zapiski Nauchnykh Seminarov POMI, 2016, Volume 448, Pages 124–134 (Mi znsl6307)  
This article is cited in 7 scientific papers (total in 7 papers)

On the generating function of discrete Chebyshev polynomials

N. Gogin, M. Hirvensalo

Department of Mathematics and Statistics, University of Turku, FI-20014 Turku, Finland
Full-text PDF (172 kB) Citations (7)
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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 the Heun differential equation, and that the closed form implies combinatorial identities that appear quite challenging to prove directly.
Key words and phrases: orthogonal polynomials, discrete Chebyshev polynomials, Krawtchouk polynomials, MacWilliams transform, generating function, Heun equation.
Funding agency Grant number
Väisälä foundation
Supported by the Väisälä foundation.
Received: 04.10.2016
English version:
Journal of Mathematical Sciences (New York), 2017, Volume 224, Issue 2, Pages 250–257
DOI: https://doi.org/10.1007/s10958-017-3410-8
Bibliographic databases:
Document Type: Article
UDC: 517.58.587
Language: English
Citation: N. Gogin, M. Hirvensalo, “On the generating function of discrete Chebyshev polynomials”, Representation theory, dynamical systems, combinatorial methods. Part XXVII, Zap. Nauchn. Sem. POMI, 448, POMI, St. Petersburg, 2016, 124–134; J. Math. Sci. (N. Y.), 224:2 (2017), 250–257
Citation in format AMSBIB
\Bibitem{GogHir16}
\by N.~Gogin, M.~Hirvensalo
\paper On the generating function of discrete Chebyshev polynomials
\inbook Representation theory, dynamical systems, combinatorial methods. Part~XXVII
\serial Zap. Nauchn. Sem. POMI
\yr 2016
\vol 448
\pages 124--134
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6307}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3576253}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2017
\vol 224
\issue 2
\pages 250--257
\crossref{https://doi.org/10.1007/s10958-017-3410-8}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85019705973}
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  • https://www.mathnet.ru/eng/znsl/v448/p124
    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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