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      A survey on pseudo-Chebyshev functions

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          Abstract

          In recent articles, by using as a starting point the Grandi (Rhodonea) curves, sets of irrational functions, extending to the fractional degree the 1st, 2nd, 3rd and 4th kind Chebyshev polynomials have been introduced. Therefore, the resulting mathematical objects are called pseudo-Chebyshev functions. In this survey, the results obtained in the above articles are presented in a compact way, in order to make the topic accessible to a wider audience. Applications in the fields of weighted best approximation, roots of 2 × 2 non-singular matrices and Fourier series are derived.

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          Most cited references 16

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          On convergence and growth of partial sums of Fourier series

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            A survey on third and fourth kind of Chebyshev polynomials and their applications

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              Chebyshev polynomials of the second, third and fourth kinds in approximation, indefinite integration, and integral transforms

               J.C. Mason (1993)
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                Author and article information

                Journal
                fopen
                https://www.4open-sciences.org
                4open
                4open
                EDP Sciences
                2557-0250
                27 April 2020
                27 April 2020
                2020
                : 3
                : ( publisher-idID: fopen/2020/01 )
                Affiliations
                [1 ] International Telematic University UniNettuno, , Corso Vittorio Emanuele II, 39, 00186 Roma, Italy,
                Author notes
                [* ]Corresponding author: paoloemilioricci@ 123456gmail.com
                Article
                fopen200001
                10.1051/fopen/2020001
                © P.E. Ricci, Published by EDP Sciences, 2020

                This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

                Page count
                Figures: 11, Tables: 0, Equations: 213, References: 21, Pages: 19
                Product
                Self URI (journal page): https://www.4open-sciences.org/
                Categories
                Review Article
                Mathematics - Applied Mathematics
                Custom metadata
                4open 2020, 3, 2
                2020
                2020
                2020

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