6 papers · 1 filter
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…
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…