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Abstract In the q^-1 q - 1 -symmetric Askey scheme, namely the q^-1 q - 1 -Askey–Wilson, continuous dual q^-1 q - 1 -Hahn, q^-1 q - 1 -Al-Salam–Chihara, continuous big q^-1 q - 1 -Hermite and continuous q^-1 q - 1 -Hermite polynomials, we compute bilateral discrete and continuous orthogonality relations. We also derive a q -beta integral which comes from the continuous orthogonality relation for the q^-1 q - 1 -Askey–Wilson polynomials. In the q 1^- q → 1 - limit, this q -beta integral corresponds to a beta integral of Ramanujan-type which we present and provide two proofs for.
Cohl et al. (Sat,) studied this question.