  Using a general $q$-summation formula, we derive a generating function for
the $q$-Hahn polynomials, which is used to give a complete proof of the
orthogonality relation for the $q$-Hahn polynomials. A new proof of the
orthogonality relation for the big $q$-Jacobi polynomials is also given. A
simple evaluation of the Nassrallah-Rahman integral is derived by using this
summation formula. A new $q$-beta integral formula is established, which
includes the Nassrallah-Rahman integral as a special case. The $q$-summation
formula also allows us to recover several strange $q$-series identities.
