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Research Article | Open Access

The infinite sums of reciprocals and the partial sums of Chebyshev polynomials

Fan Yang( ), Yang Li
School of Economics and Management, Xi'an Shiyou University, Xi'an 710065, Shaanxi, China
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Abstract

In this paper, the infinite sums of reciprocals and the partial sums derived from Chebyshev polynomials are studied. For the infinite sums of reciprocals, we apply the floor function to the reciprocals of these sums to obtain some new and interesting identities involving the Chebyshev polynomials. Simultaneously, we get several identities about the partial sums of Chebyshev polynomials by the relation of two types of Chebyshev polynomials.

Keywords

Chebyshev polynomialsreciprocalinequalityfloor function
CLC number: 11B37, 11B39

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AIMS Mathematics
Volume 7 Issue 1,
January 2022
Pages 334-348
DOI: 10.3934/math.2022023

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Cite this article:
Yang F, Li Y. The infinite sums of reciprocals and the partial sums of Chebyshev polynomials. AIMS Mathematics, 2022, 7(1): 334-348. https://doi.org/10.3934/math.2022023

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Received: 03 September 2021
Accepted: 08 October 2021
Published: 15 January 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)