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Generalizations of a terminating summation formula of basic hypergeometric series and their applications (2106.15245v1)
Published 29 Jun 2021 in math.CO and math.NT
Abstract: 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.
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