A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
On the generating function of discrete Chebyshev polynomials
Tekijät: Nikita Gogin, Mika Hirvensalo
Konferenssin vakiintunut nimi: Polynomial Computer Algebra 2016
Kustantaja: St. Petersburg Department of V. A. Steklov Mathematical Institute, Russian Academy of Sciences
Julkaisuvuosi: 2016
Journal: Zapiski Nauchnyh Seminarov Pomi
Sarjan nimi: Zapiski Nauchnykh Seminarov POMI
Vuosikerta: 448
Aloitussivu: 124
Lopetussivu: 134
ISSN: 0373-2703
eISSN: 0373-2703
Verkko-osoite: ftp://ftp.pdmi.ras.ru/pub/publicat/znsl/v448/p135.pdf
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
