On a Reduction Formula for a Kind of Double q-Integrals

Publisher： MDPI

E-ISSN： 2073-8994|8|6|44-44

ISSN： 2073-8994

Source： Symmetry, Vol.8, Iss.6, 2016-06, pp. : 44-44

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Abstract

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.