On a Reduction Formula for a Kind of Double q-Integrals
Copyright policy )On a Reduction Formula for a Kind of Double q-Integrals
Using the q-integral representation of Sears’ nonterminating extension of the q-Saalschütz summation, we derive a reduction formula for a kind of double q-integrals. This reduction formula is used to derive a curious double q-integral formula, and also allows us to prove a general q-beta integral formula including the Askey–Wilson integral formula as a special case. Using this double q-integral formula and the theory of q-partial differential equations, we derive a general q-beta integral formula, which includes the Nassrallah–Rahman integral as a special case. Our evaluation does not require the orthogonality relation for the q-Hermite polynomials and the Askey–Wilson integral formula.
- East China Normal University China (People's Republic of)
\(q\)-beta integral, \(q\)-partial differential equation, <i>q</i>-beta integral, <i>q</i>-partial differential equation, Binomial coefficients; factorials; \(q\)-identities, Basic hypergeometric functions in one variable, \({}_r\phi_s\), double \(q\)-integral, <i>q</i>-series, \(q\)-series, double <i>q</i>-integral, Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.)
\(q\)-beta integral, \(q\)-partial differential equation, <i>q</i>-beta integral, <i>q</i>-partial differential equation, Binomial coefficients; factorials; \(q\)-identities, Basic hypergeometric functions in one variable, \({}_r\phi_s\), double \(q\)-integral, <i>q</i>-series, \(q\)-series, double <i>q</i>-integral, Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.)
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