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 - 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