  We generalize a terminating summation formula to a unilateral nonterminating,
and further, a bilateral summation formula by a property of analytic functions.
The unilateral one is proved to be a $q$-analogue of a $_4F_3$-summation
formula. And, an identity unifying Jacobi's triple product identity and the
quintuple product identity is obtained as a special case of the bilateral one.
