Author:
Kim Taekyun, ,Kim Dae San,Dolgy Dmitry V.,Kwon Jongkyum, , ,
Abstract
<abstract><p>In this paper, we consider sums of finite products of the second and third type Chebyshev polynomials, those of the second and fourth type Chebyshev polynomials and those of the third and fourth type Chebyshev polynomials, and represent each of them as linear combinations of Chebyshev polynomials of all types. Here the coefficients involve some terminating hypergeometric functions $ {}_{2}F_{1} $. This problem can be viewed as a generalization of the classical linearization problems and is done by explicit computations.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Reference18 articles.
1. R. P. Agawal, D. S. Kim, T. Kim, J. Kwon, Sums of finite products of Bernoulli functions, Adv. Differ. Equ., 2017 (2017), 237.
2. G. E. Andrews, R. Askey, R. Roy, Special functions (encyclopedia of mathematics and its applications 71), Bull. London Math. Soc., 33 (2001), 116–127.
3. R. Beals, R. Wong, Special Functions and Orthogonal Polynomials, Cambridge Studies in Advanced Mathematics 153, Cambridge: Cambridge University Press, 2016.
4. G. V. Dunne, C. Schubert, Bernoulli number identities from quantum field theory and topological string theory, Commun. Number Theory Phys., 7 (2013), 225–249.
5. C. Faber, R. Pandharipande, Hodge integrals and Gromov-Witten theory, Invent. Math., 139 (2000), 173–199.
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