15 Citations (Scopus)

Abstract

Recently Ismail, Masson and Suslov established a continuous orthogonality relation and some other properties of a 2φ1-Bessel function on a q-quadratic grid. Askey suggested that the 'Bessel-type orthogonality' found in the above paper at the 2φ1-level really has a general character and can be extended up to the 8φ7-level. Very well poised 8φ7-fuctions are known as a nonterminating version of the classical Askey-Wilson polynomials. In this paper we prove Askey's conjecture and discuss some properties of the orthogonal 8φ7-functions. Another type of the orthogonality relation for a very well poised 87-function was recently found by Askey, Rahman and Suslov.

Original languageEnglish (US)
Pages (from-to)5877-5885
Number of pages9
JournalJournal of Physics A: Mathematical and General
Volume30
Issue number16
DOIs
StatePublished - Aug 21 1997

Fingerprint

Orthogonal functions
Orthogonality Relations
Bessel functions
orthogonality
Polynomials
Askey-Wilson Polynomials
Orthogonal Functions
Friedrich Wilhelm Bessel
Bessel Functions
Orthogonality
Grid
polynomials
grids
Character

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Some orthogonal very well poised 8φ7-functions. / Suslov, Sergei.

In: Journal of Physics A: Mathematical and General, Vol. 30, No. 16, 21.08.1997, p. 5877-5885.

Research output: Contribution to journalArticle

@article{0b0f68f2c87946468022217dcfc41bf0,
title = "Some orthogonal very well poised 8φ7-functions",
abstract = "Recently Ismail, Masson and Suslov established a continuous orthogonality relation and some other properties of a 2φ1-Bessel function on a q-quadratic grid. Askey suggested that the 'Bessel-type orthogonality' found in the above paper at the 2φ1-level really has a general character and can be extended up to the 8φ7-level. Very well poised 8φ7-fuctions are known as a nonterminating version of the classical Askey-Wilson polynomials. In this paper we prove Askey's conjecture and discuss some properties of the orthogonal 8φ7-functions. Another type of the orthogonality relation for a very well poised 87-function was recently found by Askey, Rahman and Suslov.",
author = "Sergei Suslov",
year = "1997",
month = "8",
day = "21",
doi = "10.1088/0305-4470/30/16/027",
language = "English (US)",
volume = "30",
pages = "5877--5885",
journal = "Journal of Physics A: Mathematical and Theoretical",
issn = "1751-8113",
publisher = "IOP Publishing Ltd.",
number = "16",

}

TY - JOUR

T1 - Some orthogonal very well poised 8φ7-functions

AU - Suslov, Sergei

PY - 1997/8/21

Y1 - 1997/8/21

N2 - Recently Ismail, Masson and Suslov established a continuous orthogonality relation and some other properties of a 2φ1-Bessel function on a q-quadratic grid. Askey suggested that the 'Bessel-type orthogonality' found in the above paper at the 2φ1-level really has a general character and can be extended up to the 8φ7-level. Very well poised 8φ7-fuctions are known as a nonterminating version of the classical Askey-Wilson polynomials. In this paper we prove Askey's conjecture and discuss some properties of the orthogonal 8φ7-functions. Another type of the orthogonality relation for a very well poised 87-function was recently found by Askey, Rahman and Suslov.

AB - Recently Ismail, Masson and Suslov established a continuous orthogonality relation and some other properties of a 2φ1-Bessel function on a q-quadratic grid. Askey suggested that the 'Bessel-type orthogonality' found in the above paper at the 2φ1-level really has a general character and can be extended up to the 8φ7-level. Very well poised 8φ7-fuctions are known as a nonterminating version of the classical Askey-Wilson polynomials. In this paper we prove Askey's conjecture and discuss some properties of the orthogonal 8φ7-functions. Another type of the orthogonality relation for a very well poised 87-function was recently found by Askey, Rahman and Suslov.

UR - http://www.scopus.com/inward/record.url?scp=0041157559&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0041157559&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/30/16/027

DO - 10.1088/0305-4470/30/16/027

M3 - Article

AN - SCOPUS:0041157559

VL - 30

SP - 5877

EP - 5885

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 16

ER -