scholarly journals Pearson equations for discrete orthogonal polynomials: I. Generalized hypergeometric functions and Toda equations

2021 ◽  
Author(s):  
Manuel Mañas ◽  
Itsaso Fernández‐Irisarri ◽  
Omar F. González‐Hernández
Keyword(s):  
Orthogonal Polynomials ◽  
Hypergeometric Functions ◽  
Generalized Hypergeometric Functions ◽  
Discrete Orthogonal Polynomials ◽  
Discrete Orthogonal ◽  
Toda Equations

Orthogonal Polynomials in Mathematical Physics

2018 ◽  
Vol 30 (06) ◽  
pp. 1840005 ◽  
Author(s):  
Chuan-Tsung Chan ◽  
A. Mironov ◽  
A. Morozov ◽  
A. Sleptsov
Keyword(s):  
Orthogonal Polynomials ◽  
Hypergeometric Functions ◽  
Knot Theory ◽  
Virasoro Algebra ◽  
Integral Representations ◽  
Conformal Blocks ◽  
Generic Framework ◽  
Integrable Theory ◽  
Discrete Orthogonal Polynomials ◽  
Discrete Orthogonal

This is a review of ([Formula: see text]-)hypergeometric orthogonal polynomials and their relation to representation theory of quantum groups, to matrix models, to integrable theory, and to knot theory. We discuss both continuous and discrete orthogonal polynomials, and consider their various generalizations. The review also includes the orthogonal polynomials into a generic framework of ([Formula: see text]-)hypergeometric functions and their integral representations. In particular, this gives rise to relations with conformal blocks of the Virasoro algebra. To the memory of Ludwig Dmitrievich Faddeev

Stieltjes’ theorem for classical discrete orthogonal polynomials

2020 ◽  
Vol 61 (10) ◽  
pp. 103505
Author(s):  
K. Castillo ◽  
F. R. Rafaeli ◽  
A. Suzuki
Keyword(s):  
Orthogonal Polynomials ◽  
Discrete Orthogonal Polynomials ◽  
Discrete Orthogonal
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