Quantum Groups, q-Orthogonal Polynomials and Basic Hypergeometric Functions

1992 ◽  
pp. 1-136
Author(s):  
N. Ja. Vilenkin ◽  
A. U. Klimyk
Keyword(s):  
Orthogonal Polynomials ◽  
Quantum Groups ◽  
Hypergeometric Functions ◽  
Basic Hypergeometric Functions

scholarly journals The Many Faces of the Chiral Potts Model

1997 ◽  
Vol 11 (01n02) ◽  
pp. 11-26 ◽  
Author(s):  
Helen Au-Yang ◽  
Jacques H.H. Perk
Keyword(s):  
Quantum Groups ◽  
Potts Model ◽  
Hypergeometric Functions ◽  
Chiral Potts Model ◽  
Root Of Unity ◽  
Basic Hypergeometric Functions ◽  
Higher Genus ◽  
The Many

In this talk, we give a brief overview of several aspects of the theory of the chiral Potts model, including higher-genus solutions of the star–triangle and tetrahedron equations, cyclic representations of affine quantum groups, basic hypergeometric functions at root of unity, and possible applications.

q-Integral and Moment Representations for q-Orthogonal Polynomials

2002 ◽  
Vol 54 (4) ◽  
pp. 709-735 ◽  
Author(s):  
Mourad E. H. Ismail ◽  
Dennis Stanton
Keyword(s):  
Orthogonal Polynomials ◽  
Exponential Function ◽  
Generating Functions ◽  
Hypergeometric Functions ◽  
Integral Representations ◽  
Basic Hypergeometric Functions ◽  
Transformation Formulas

AbstractWe develop a method for deriving integral representations of certain orthogonal polynomials as moments. These moment representations are applied to find linear and multilinear generating functions for q-orthogonal polynomials. As a byproduct we establish new transformation formulas for combinations of basic hypergeometric functions, including a new representation of the q-exponential function εq.

scholarly journals Neoteric formulas of the monic orthogonal Chebyshev polynomials of the sixth-kind involving moments and linearization formulas

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Waleed M. Abd-Elhameed ◽  
Youssri H. Youssri
Keyword(s):  
Orthogonal Polynomials ◽  
Chebyshev Polynomials ◽  
Hypergeometric Functions ◽  
Connection Coefficients ◽  
Current Article ◽  
In Virtue Of ◽  
Connection Formulas

AbstractThe principal aim of the current article is to establish new formulas of Chebyshev polynomials of the sixth-kind. Two different approaches are followed to derive new connection formulas between these polynomials and some other orthogonal polynomials. The connection coefficients are expressed in terms of terminating hypergeometric functions of certain arguments; however, they can be reduced in some cases. New moment formulas of the sixth-kind Chebyshev polynomials are also established, and in virtue of such formulas, linearization formulas of these polynomials are developed.

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