Bilateral discrete and continuous orthogonality relations in the $$q^{-1}$$-symmetric Askey scheme
Year: 2025
Type: article
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 $$q\rightarrow 1^{-}$$ q → 1 - limit, this q -beta integral corresponds to a beta integral of Ramanujan-type which we present and provide two proofs for.
Source: Arabian Journal of Mathematics
Authors: Howard S. Cohl, Hans Volkmer
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4416814574