On the Askey–Wilson polynomials and a 𝑞-beta integral
Copyright policy )On the Askey–Wilson polynomials and a 𝑞-beta integral
A proof of the orthogonality relation for the Askey–Wilson polynomials is given by using a generating function for the Askey–Wilson polynomials and the uniqueness of a rational function expansion. We further use the orthogonality relation for the Askey–Wilson polynomials and a q q -series transformation formula to evaluate a general q q -beta integral with eight parameters. The integrand of this q q -beta integral is the product of two terminating 5 ϕ 4 _5\phi _4 series and the value is a 10 ϕ 9 _{10}\phi _9 series.
- East China Normal University China (People's Republic of)
\(q\)-beta integral, Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), Askey-Wilson polynomials, double \(q\)-series, Basic hypergeometric functions in one variable, \({}_r\phi_s\), Binomial coefficients; factorials; \(q\)-identities, \(q\)-calculus and related topics, Askey-Wilson integral, Sums of squares and representations by other particular quadratic forms
\(q\)-beta integral, Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), Askey-Wilson polynomials, double \(q\)-series, Basic hypergeometric functions in one variable, \({}_r\phi_s\), Binomial coefficients; factorials; \(q\)-identities, \(q\)-calculus and related topics, Askey-Wilson integral, Sums of squares and representations by other particular quadratic forms
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