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We prove a general quadratic formula for basic hypergeometric series, fromwhich simple proofs of several recent determinant and Pfaffian formulas areobtained. A special case of the quadratic formula is actually related to a Gramdeterminant formula for Askey-Wilson polynomials. We also show how to derive arecent double-sum formula for the moments of Askey-Wilson polynomials fromNewton's interpolation formula.

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