| Issue |
4open
Volume 3, 2020
|
|
|---|---|---|
| Article Number | 2 | |
| Number of page(s) | 19 | |
| Section | Mathematics - Applied Mathematics | |
| DOI | https://doi.org/10.1051/fopen/2020001 | |
| Published online | 27 April 2020 | |
Review Article
A survey on pseudo-Chebyshev functions
International Telematic University UniNettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy
* Corresponding author: paoloemilioricci@gmail.com
Received:
9
January
2020
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.