5 citations · 12 across the 13 of their papers we have counts for
13 papers
On an expansion formula of Liu
Bing He
In this paper, we extend an expansion formula of Liu to multiple basic hypergeometric series over the root system The usefulness of Liu's expansion formula in special func…
Proofs for certain conjectures of Gosper on q-trigonometric identities
Bing He
Applying the theory of elliptic functions we establish two Jacobi theta function identities. From these identities we confirm two q-trigonometric identities conjectured by Gosper.…
Hecke-type identities associated with definite quadratic forms
Bing He
Since the study by Jacobi and Hecke, Hecke-type series have received a lot of attention. Unlike such series associated with indefinite quadratic forms, identities on Hecke-type ser…
Hecke-type series involving infinite products
Bing He
Since the study by Jacobi and Hecke, Hecke-type series have received extensive attention. Especially, Hecke-type series involving infinite products have attracted broad interest am…
On certain q-trigonometric identities
Bing He
Finding theta function (or -)analogues for well-known trigonometric identities is an interesting topic. In this paper, we first introduce the definition of -analogues for $\m…
Proofs for two Lambert series identities of Gosper
Bing He
Applying the theory of modular forms and Lambert series manipulations we establish an Eisenstein series identity. From this formula we confirm a Lambert series identity conjectured…
Some truncated identities of Gauss
Bing He
Motivated by the works of Andrews-Merca and Guo-Zeng, we establish some truncated identities of Gauss by using some summation formulas from the works of Zhi-Guo Liu. These give thr…
Two q-summation formulas and q-analogues of series expansions for certain constants
Bing He, Hongcun Zhai
From two q-summation formulas we deduce certain series expansion formulas involving the q-gamma function. With these formulas we can give q-analogues of series expansions for certa…
An addition formula for the Jacobian theta function with applications
Bing He, Hongcun Zhai
Liu established an addition formula for the Jacobian theta function by using the theory of elliptic functions. From this addition formula he obtained the Ramanujan cubic theta func…
A finite field analogue for Appell series F_3
Bing He
In this paper we introduce a finite field analogue for the Appell series F_3 and give some reduction formulae and certain generating functions for this function over finite fields.
A Lauricella hypergeometric series over finite fields
Bing He
In this paper we introduce a finite field analogue of a Lauricella hypergeometric series. An integral formula for the Lauricella hypergeometric series and its finite field analogue…
An Appell series over finite fields
Bing He, Long Li, Ruiming Zhang
In this paper we present a finite field analogue for one of the Appell series. We shall derive its transformations, reduction formulas as well as generating functions.
On zeros of some entire functions
Bing He
Let \begin{equation*} A_{q}^{(α)}(a;z) = \sum_{k=0}^{\infty} \frac{(a;q)_{k} q^{αk^2} z^k} {(q;q)_{k}}, \end{equation*} where In a paper of Ruiming Zhang, he asked un…