Sums of finite products of Chebyshev polynomials of the third and fourth kinds

In this paper, we study sums of finite products of Chebyshev polynomials of the third and fourth kinds and obtain Fourier series expansions of functions associated with them. Then from these Fourier series expansions we will be able to express those sums of finite products as linear combinations of...

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Bibliographic Details
Published in:Advances in difference equations 2018-08, Vol.2018 (1), p.1-17, Article 283
Main Authors: Kim, Taekyun, Kim, Dae San, Dolgy, Dmitry V., Kwon, Jongkyum
Format: Article
Language:English
Subjects:
Analysis
Chebyshev approximation
Chebyshev polynomials
Difference and Functional Equations
Fourier series
Functional Analysis
Ice
Mathematical analysis
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Polynomials
Sums
Sums of finite products of Chebyshev polynomials of the third and fourth kinds
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Summary:In this paper, we study sums of finite products of Chebyshev polynomials of the third and fourth kinds and obtain Fourier series expansions of functions associated with them. Then from these Fourier series expansions we will be able to express those sums of finite products as linear combinations of Bernoulli polynomials and to have some identities from those expressions.
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-018-1747-z