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math.CO2021
A new semi-finite form of the quintuple product identity
Jun-Ming Zhu
The quintuple product identity are deduced from a new semi-finite form, which are obtained from the very-well-poised series.
math.HO2021
A semi-finite proof of Jacobi's triple product identity
Jun-Ming Zhu
Jacobi's triple product identity is proved from one of Euler's -exponential functions in an elementary way.
math.CO2021
Generalizations of a terminating summation formula of basic hypergeometric series and their applications
Jun-Ming Zhu
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…
math.CO2021
An alternate circular summation formula of theta functions and its applications
Jun-Ming Zhu
We prove a general alternate circular summation formula of theta functions, which implies a great deal of theta-function identities. In particular, we recover several identities in…