Bailey's well-poised 6[formula omitted]-series implies the Askey–Wilson integral

Abstract

Bailey's fundamental identity of bilateral well-poised ψ 6 6 -series is utilized to present shorter proofs for the two important q-beta integrals discovered by Askey and Wilson (1985) [4] and Askey (1987) [3]. Another rather general q-beta integral containing many extra parameters is similarly derived from Chu's extended Karlsson–Minton-type identity for a bilateral well-poised ψ 2 n + 6 6 + 2 n -series.