Multivariable Askey–Wilson function and bispectrality

For every positive integer d , we define a meromorphic function F d ( n ; z ), where n , z ∈ℂ d , which is a natural extension of the multivariable Askey–Wilson polynomials of Gasper and Rahman (Theory and Applications of Special Functions, Dev. Math., vol. 13, pp. 209–219, Springer, New York, 2005...

Celý popis

Uloženo v:
Podrobná bibliografie
Vydáno v:The Ramanujan journal Ročník 24; číslo 3; s. 273 - 287
Hlavní autoři: Geronimo, Jeffrey S., Iliev, Plamen
Médium: Journal Article
Jazyk:angličtina
Vydáno: Boston Springer US 01.04.2011
Témata:
Combinatorics
Field Theory and Polynomials
Fourier Analysis
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
Number Theory
Bispectrality
33D50
Basic hypergeometric series
Multivariable orthogonal polynomials
39A70
ISSN:1382-4090, 1572-9303
On-line přístup:Získat plný text
Tagy: Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
Popis
Shrnutí:For every positive integer d , we define a meromorphic function F d ( n ; z ), where n , z ∈ℂ d , which is a natural extension of the multivariable Askey–Wilson polynomials of Gasper and Rahman (Theory and Applications of Special Functions, Dev. Math., vol. 13, pp. 209–219, Springer, New York, 2005 ). It is defined as a product of very-well-poised 8 φ 7 series and we show that it is a common eigenfunction of two commutative algebras and of difference operators acting on z and n , with eigenvalues depending on n and z , respectively. In particular, this leads to certain identities connecting products of very-well-poised 8 φ 7 series.
ISSN:1382-4090
1572-9303
DOI:10.1007/s11139-010-9244-3