### Abstract

We prove a general quadratic formula for basic hypergeometric series, from which simple proofs of several recent determinant and Pfaffian formulas are obtained. A special case of the quadratic formula is actually related to a Gram determinant formula for Askey-Wilson polynomials. We also show how to derive a recent double-sum formula for the moments of Askey- Wilson polynomials from Newton’s interpolation formula.

Original language | English |
---|---|

Pages (from-to) | 2003-2015 |

Number of pages | 13 |

Journal | Proceedings of the American Mathematical Society |

Volume | 143 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2015 |

Externally published | Yes |

### Fingerprint

### Keywords

- Askey-Wilson polynomials
- Desnanot–Jacobi adjoint matrix theorem
- Gram determinants
- Moments of Askey-Wilson polynomials
- Pfaffians
- Quadratic formula of basic hypergeometric series

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Proceedings of the American Mathematical Society*,

*143*(5), 2003-2015. https://doi.org/10.1090/S0002-9939-2015-12099-0

**A quadratic formula for basic hypergeometric series related to Askey-Wilson polynomials.** / Guo, Victor J W; Ishikawa, Masao; Tagawa, Hiroyuki; Zeng, Jiang.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 143, no. 5, pp. 2003-2015. https://doi.org/10.1090/S0002-9939-2015-12099-0

}

TY - JOUR

T1 - A quadratic formula for basic hypergeometric series related to Askey-Wilson polynomials

AU - Guo, Victor J W

AU - Ishikawa, Masao

AU - Tagawa, Hiroyuki

AU - Zeng, Jiang

PY - 2015

Y1 - 2015

N2 - We prove a general quadratic formula for basic hypergeometric series, from which simple proofs of several recent determinant and Pfaffian formulas are obtained. A special case of the quadratic formula is actually related to a Gram determinant formula for Askey-Wilson polynomials. We also show how to derive a recent double-sum formula for the moments of Askey- Wilson polynomials from Newton’s interpolation formula.

AB - We prove a general quadratic formula for basic hypergeometric series, from which simple proofs of several recent determinant and Pfaffian formulas are obtained. A special case of the quadratic formula is actually related to a Gram determinant formula for Askey-Wilson polynomials. We also show how to derive a recent double-sum formula for the moments of Askey- Wilson polynomials from Newton’s interpolation formula.

KW - Askey-Wilson polynomials

KW - Desnanot–Jacobi adjoint matrix theorem

KW - Gram determinants

KW - Moments of Askey-Wilson polynomials

KW - Pfaffians

KW - Quadratic formula of basic hypergeometric series

UR - http://www.scopus.com/inward/record.url?scp=84923239760&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84923239760&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-2015-12099-0

DO - 10.1090/S0002-9939-2015-12099-0

M3 - Article

AN - SCOPUS:84923239760

VL - 143

SP - 2003

EP - 2015

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 5

ER -