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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 $_4F_3$-summationformula. And, an identity unifying Jacobi's triple product identity and thequintuple product identity is obtained as a special case of the bilateral one.

Generalizations of a terminating summation formula of basic hypergeometric series and their applications