### 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 |
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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 - Jan 1 2015 |

Externally published | Yes |

### 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

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## Cite this

Guo, V. J. W., Ishikawa, M., Tagawa, H., & Zeng, J. (2015). A quadratic formula for basic hypergeometric series related to Askey-Wilson polynomials.

*Proceedings of the American Mathematical Society*,*143*(5), 2003-2015. https://doi.org/10.1090/S0002-9939-2015-12099-0