Lectures on Orthogonal Polynomials and Special Functions

2020 ◽  
Keyword(s):  
Orthogonal Polynomials ◽  
Special Functions

scholarly journals Preface: Orthogonal polynomials, special functions, and applications

2018 ◽  
Vol 141 (4) ◽  
pp. 421-423
Author(s):  
Peter A. Clarkson ◽  
Adri B. Olde Daalhuis
Keyword(s):  
Orthogonal Polynomials ◽  
Special Functions

Special Functions and Orthogonal Polynomials

2009 ◽  
pp. 261-268
Author(s):  
Inna Shingareva ◽  
Carlos Lizárraga-Celaya
Keyword(s):  
Orthogonal Polynomials ◽  
Special Functions

scholarly journals ON CONNECTING WEYL-ORBIT FUNCTIONS TO JACOBI POLYNOMIALS AND MULTIVARIATE (ANTI)SYMMETRIC TRIGONOMETRIC FUNCTIONS

2016 ◽  
Vol 56 (4) ◽  
pp. 283-290 ◽  
Author(s):  
Jiri Hrivnak ◽  
Lenka Motlochova
Keyword(s):  
Orthogonal Polynomials ◽  
Chebyshev Polynomials ◽  
Jacobi Polynomials ◽  
Special Functions ◽  
The Other ◽  
Trigonometric Functions ◽  
The One ◽  
Sine Functions

<p>The aim of this paper is to make an explicit link between the Weyl-orbit functions and the corresponding polynomials, on the one hand, and to several other families of special functions and orthogonal polynomials on the other. The cornerstone is the connection that is made between the one-variable orbit functions of <em>A<sub>1</sub></em> and the four kinds of Chebyshev polynomials. It is shown that there exists a similar connection for the two-variable orbit functions of <em>A<sub>2</sub></em> and a specific version of two variable Jacobi polynomials. The connection with recently studied <em>G<sub>2</sub></em>-polynomials is established. Formulas for connection between the four types of orbit functions of <em>B<sub>n</sub></em> or <em>C<sub>n</sub></em> and the (anti)symmetric multivariate cosine and sine functions are explicitly derived.</p>

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