A1 Refereed original research article in a scientific journal

On the generating function of discrete Chebyshev polynomials



Authors: Nikita Gogin, Mika Hirvensalo

Conference name: Polynomial Computer Algebra 2016

Publisher: St. Petersburg Department of V. A. Steklov Mathematical Institute, Russian Academy of Sciences

Publication year: 2016

Journal: Zapiski Nauchnyh Seminarov Pomi

Series title: Zapiski Nauchnykh Seminarov POMI

Volume: 448

First page : 124

Last page: 134

ISSN: 0373-2703

eISSN: 0373-2703

Web address : ftp://ftp.pdmi.ras.ru/pub/publicat/znsl/v448/p135.pdf


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



Last updated on 2024-26-11 at 23:22