6 papers
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.
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.
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…
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…
Cohomology and deformations of 3-dimensional Heisenberg Hom-Lie superalgebras
Junxia Zhu, Liangyun Chen
In this paper, we study Hom-Lie superalgebras of Heisenberg type. For 3-dimensional Heisenberg Hom-Lie superalgebras, we describe their Hom-Lie super structures, compute the cohomo…
The number of convex pentagons and hexagons in an -triangular net
Jun-Ming Zhu
In this paper, we obtain the counting formulaes of convex pentagons and convex hexagons, respectively, in an -triangular net by solving the corresponding recursive formulaes.