A Fourier series kernel based on Chebyshev polynomials

Computing ◽  
1977 ◽  
Vol 18 (1) ◽  
pp. 37-50
Author(s):  
E. Rietsch
Keyword(s):  
Fourier Series ◽  
Chebyshev Polynomials

Delving Deeper: The Chebyshev Polynomials: Patterns and Derivation

2004 ◽  
Vol 98 (1) ◽  
pp. 20-25 ◽  
Author(s):  
Benjamin Sinwell
Keyword(s):  
High School ◽  
Number Theory ◽  
Graph Theory ◽  
Fourier Series ◽  
High School Teachers ◽  
Chebyshev Polynomials ◽  
Mathematical Community ◽  
Russian Mathematician ◽  
School Teachers ◽  
Mathematical Exploration

Pafnuty Lvovich Chebyshev, a Russian mathematician, is famous for his work in the area of number theory and for his work on a sequence of polynomials that now bears his name. These Chebyshev polynomials have applications in the fields of polynomial approximation, numerical analysis, graph theory, Fourier series, and many other areas. They can be derived directly from the multiple-angle formulas for sine and cosine. They are relevant in high school and in the broader mathematical community. For this reason, the Chebyshev polynomials were chosen as one of the topics for study at the 2003 High School Teachers Program at the Park City Mathematics Institute (PCMI). The following is a derivation of the Chebyshev polynomials and a mathematical exploration of the patterns that they produce.

scholarly journals Fourier Series for Functions Related to Chebyshev Polynomials of the First Kind and Lucas Polynomials

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 276 ◽  
Author(s):  
Taekyun Kim ◽  
Dae Kim ◽  
Lee-Chae Jang ◽  
Gwan-Woo Jang
Keyword(s):  
Fourier Series ◽  
Chebyshev Polynomials ◽  
Bernoulli Polynomials ◽  
Series Expansions ◽  
Linear Combinations ◽  
Lucas Polynomials ◽  
Finite Products ◽  
Derive Fourier Series

In this paper, we derive Fourier series expansions for functions related to sums of finite products of Chebyshev polynomials of the first kind and of Lucas polynomials. From the Fourier series expansions, we are able to express those two kinds of sums of finite products of polynomials as linear combinations of Bernoulli polynomials.

scholarly journals Fejér and Dirichlet Kernels: Their Associated Polynomials

2009 ◽  
Vol 1 (2) ◽  
pp. 281-284
Author(s):  
M. Galaz-Larios ◽  
R. Garcia-Olivo ◽  
J. López-Bonilla
Keyword(s):  
Fourier Series ◽  
Chebyshev Polynomials ◽  
Fejér Kernel ◽  
Associated Polynomials

We show that the Fejér kernel generates the fifth-kind Chebyshev polynomials.Keywords: Kernels in Fourier series; Chebyshev polynomials.© 2009 JSR Publications.ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved. DOI: 10.3329/jsr.v1i2.2282

scholarly journals A survey on pseudo-Chebyshev functions

4open ◽  
2020 ◽  
Vol 3 ◽  
pp. 2 ◽  
Author(s):  
Paolo Emilio Ricci
Keyword(s):  
Fourier Series ◽  
Chebyshev Polynomials ◽  
Best Approximation ◽  
Mathematical Objects ◽  
Starting Point ◽  
Singular Matrices ◽  
Chebyshev Functions

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.

Topology Optimization of IPM Motors using Fourier Series

2017 ◽  
Vol 137 (3) ◽  
pp. 245-253
Author(s):  
Hidenori Sasaki ◽  
Hajime Igarashi
Keyword(s):  
Fourier Series ◽  
Topology Optimization

The maximal operator of the Marcinkiewicz-Fejér means of the 2-dimensional Vilenkin-Fourier series

2008 ◽  
Vol 45 (3) ◽  
pp. 321-331
Author(s):  
István Blahota ◽  
Ushangi Goginava
Keyword(s):  
Fourier Series ◽  
Hardy Space ◽  
Maximal Operator ◽  
Fejér Means

In this paper we prove that the maximal operator of the Marcinkiewicz-Fejér means of the 2-dimensional Vilenkin-Fourier series is not bounded from the Hardy space H2/3 ( G2 ) to the space L2/3 ( G2 ).

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