Sums of finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials

In this paper, we consider sums of finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials and derive Fourier series expansions of functions associated with them. From these Fourier series expansions, we can express those sums of finite products in terms of Bernoulli...

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Bibliographic Details
Published in:Journal of inequalities and applications 2018, Vol.2018 (1), p.1-14, Article 148
Main Authors: Kim, Taekyun, Kim, Dae San, Dolgy, Dmitry V., Park, Jin-Woo
Format: Article
Language:English
Subjects:
Analysis
Applications of Mathematics
Chebyshev approximation
Chebyshev polynomials of the second kind
Fibonacci numbers
Fibonacci polynomials
Fourier series
Mathematical analysis
Mathematics
Mathematics and Statistics
Polynomials
Sums
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Summary:In this paper, we consider sums of finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials and derive Fourier series expansions of functions associated with them. From these Fourier series expansions, we can express those sums of finite products in terms of Bernoulli polynomials and obtain some identities by using those expressions.
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-018-1744-5