Volume 3, 2020
|Number of page(s)||19|
|Section||Mathematics - Applied Mathematics|
|Published online||27 April 2020|
A survey on pseudo-Chebyshev functions
International Telematic University UniNettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy
* Corresponding author: firstname.lastname@example.org
Accepted: 11 February 2020
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.
Key words: Grandi curves / Pseudo-Chebyshev functions / Recurrence relations / Differential equations / Orthogonality properties
© 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.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.