A new proof of the Nassrallah-Rahman integral. (Chinese. English summary) Zbl 1010.33009

Summary: Two identities of the \(q\)-differential operator are proved by using the Leibniz rule for the \(a\)-differential operator. With these two operator identities and some well-known summation formulas for \(q\)-series, a new proof of the Nassrallah-Rahman integral is given. Finally, an easy evaluation of Nassrallah and Rahman’s integral representation for \(q\)-series \(_8\Phi_7\) is given.


33D45 Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)