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- Title
Representation by Chebyshev Polynomials for Sums of Finite Products of Chebyshev Polynomials.
- Authors
Kim, Taekyun; Kim, Dae San; Jang, Lee-Chae; Dolgy, Dmitry V.
- Abstract
In this paper, we consider sums of finite products of Chebyshev polynomials of the first, third, and fourth kinds, which are different from the previously-studied ones. We represent each of them as linear combinations of Chebyshev polynomials of all kinds whose coefficients involve some terminating hypergeometric functions 2 F 1 . The results may be viewed as a generalization of the linearization problem, which is concerned with determining the coefficients in the expansion of the product of two polynomials in terms of any given sequence of polynomials. These representations are obtained by explicit computations.
- Subjects
INTEGERS; LINEAR equations; CHEBYSHEV polynomials; MATHEMATICAL functions; CHEBYSHEV systems
- Publication
Symmetry (20738994), 2018, Vol 10, Issue 12, p742
- ISSN
2073-8994
- Publication type
Article
- DOI
10.3390/sym10120742