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.
- Askey-Wilson polynomials
- Desnanot–Jacobi adjoint matrix theorem
- Gram determinants
- Moments of Askey-Wilson polynomials
- Quadratic formula of basic hypergeometric series
ASJC Scopus subject areas
- Applied Mathematics