3 papers
math.NT2018
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…
math.NT2018
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…
math.NT2018
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…