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...
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| Vydané v: | The Ramanujan journal Ročník 24; číslo 3; s. 273 - 287 |
|---|---|
| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Boston
Springer US
01.04.2011
|
| Predmet: | |
| ISSN: | 1382-4090, 1572-9303 |
| On-line prístup: | Získať plný text |
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| 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 |