4 citations · 5 across the 8 of their papers we have counts for
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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.
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…
A note on a generalized circular summation formula of theta functions
Jun-Ming Zhu
In this note, we make a correction of the imaginary transformation formula of Chan and Liu's circular formula of theta functions. We also get the imaginary transformation formulaes…
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.
The solutions of four -functional equations
Jun-Ming Zhu
In this note we obtain the solutions of four -functional equations and express the solutions in -operator forms. These equations give sufficient conditions for -operator m…