### Abstract

In a recent paper Ismail et al. (Algebraic Methods and q-Special Functions (J.F. van Diejen and L. Vinet, eds.) CRM Preceding and Lecture Notes, Vol. 22. American Mathematical Society, 1999, pp. 183-200) have established a continuous orthogonality relation and some other properties of a 2φ1-Bessel function on a q-quadratic grid. Dick Askey (private communication) suggested that the "Bessel-type orthogonality" found in Ismail et al. (1999) at the 2φ1-level has really a general character and can be extended up to the 8φ7-level. Very-well-poised 8φ7-functions are known as a nonterminating version of the classical Askey-Wilson polynomials (SIAM J. Math. Anal. 10 (1979), 1008-1016; Memoirs Amer. Math. Soc. Number 319 (1985)). Askey's conjecture has been proved by the author in J. Phys. A: Math. Gen. 30 (1997), 5877-5885. In the present paper which is an extended version of Suslov (1997) we discuss in detail properties of the orthogonal 8φ7-functions. Another type of the orthogonality relation for a very-well-poised 8φ7-function was recently found by Askey et al. J. Comp. Appl. Math. 68 (1996), 25-55.

Original language | English (US) |
---|---|

Pages (from-to) | 183-218 |

Number of pages | 36 |

Journal | Ramanujan Journal |

Volume | 5 |

Issue number | 2 |

DOIs | |

State | Published - Jun 2001 |

### Fingerprint

### Keywords

- Askey-Wilson polynomials
- Basic hypergeometric series
- Orthogonal functions
- q-Bessel functions

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

**Some orthogonal very-well-poised _{8φ7}-functions that generalize Askey-Wilson polynomials.** / Suslov, Sergei.

Research output: Contribution to journal › Article

_{8φ7}-functions that generalize Askey-Wilson polynomials',

*Ramanujan Journal*, vol. 5, no. 2, pp. 183-218. https://doi.org/10.1023/A:1011439924912

}

TY - JOUR

T1 - Some orthogonal very-well-poised 8φ7-functions that generalize Askey-Wilson polynomials

AU - Suslov, Sergei

PY - 2001/6

Y1 - 2001/6

N2 - In a recent paper Ismail et al. (Algebraic Methods and q-Special Functions (J.F. van Diejen and L. Vinet, eds.) CRM Preceding and Lecture Notes, Vol. 22. American Mathematical Society, 1999, pp. 183-200) have established a continuous orthogonality relation and some other properties of a 2φ1-Bessel function on a q-quadratic grid. Dick Askey (private communication) suggested that the "Bessel-type orthogonality" found in Ismail et al. (1999) at the 2φ1-level has really a general character and can be extended up to the 8φ7-level. Very-well-poised 8φ7-functions are known as a nonterminating version of the classical Askey-Wilson polynomials (SIAM J. Math. Anal. 10 (1979), 1008-1016; Memoirs Amer. Math. Soc. Number 319 (1985)). Askey's conjecture has been proved by the author in J. Phys. A: Math. Gen. 30 (1997), 5877-5885. In the present paper which is an extended version of Suslov (1997) we discuss in detail properties of the orthogonal 8φ7-functions. Another type of the orthogonality relation for a very-well-poised 8φ7-function was recently found by Askey et al. J. Comp. Appl. Math. 68 (1996), 25-55.

AB - In a recent paper Ismail et al. (Algebraic Methods and q-Special Functions (J.F. van Diejen and L. Vinet, eds.) CRM Preceding and Lecture Notes, Vol. 22. American Mathematical Society, 1999, pp. 183-200) have established a continuous orthogonality relation and some other properties of a 2φ1-Bessel function on a q-quadratic grid. Dick Askey (private communication) suggested that the "Bessel-type orthogonality" found in Ismail et al. (1999) at the 2φ1-level has really a general character and can be extended up to the 8φ7-level. Very-well-poised 8φ7-functions are known as a nonterminating version of the classical Askey-Wilson polynomials (SIAM J. Math. Anal. 10 (1979), 1008-1016; Memoirs Amer. Math. Soc. Number 319 (1985)). Askey's conjecture has been proved by the author in J. Phys. A: Math. Gen. 30 (1997), 5877-5885. In the present paper which is an extended version of Suslov (1997) we discuss in detail properties of the orthogonal 8φ7-functions. Another type of the orthogonality relation for a very-well-poised 8φ7-function was recently found by Askey et al. J. Comp. Appl. Math. 68 (1996), 25-55.

KW - Askey-Wilson polynomials

KW - Basic hypergeometric series

KW - Orthogonal functions

KW - q-Bessel functions

UR - http://www.scopus.com/inward/record.url?scp=0035539589&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035539589&partnerID=8YFLogxK

U2 - 10.1023/A:1011439924912

DO - 10.1023/A:1011439924912

M3 - Article

VL - 5

SP - 183

EP - 218

JO - Ramanujan Journal

JF - Ramanujan Journal

SN - 1382-4090

IS - 2

ER -