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Some remarks on $q$-beta integral

Some remarks on $q$-beta integral

The following $q$-integral \[ \int _{ - c}^d {\frac {{{{( - qt/c)}_{\alpha - 1}}{{(qt/d)}_{\beta - 1}}}} {{{{( - qet)}_{\alpha + \beta }}}}} {d_q}t\] is evaluated. A more general $q$-integral is also considered. Some applications to the $q$-Wilson (or Askey-Wilson) polynomials are also given.