105 citations · 168 across the 35 of their papers we have counts for
5 papers · 1 filter
Supercongruences arising from hypergeometric series identities
Ji-Cai Liu
By using some hypergeometric series identities, we prove two supercongruences on truncated hypergeometric series, one of which is related to a modular Calabi--Yau threefold, and th…
On van Hamme's (A.2) and (H.2) supercongruences
Ji-Cai Liu
In 1997, van Hamme conjectured 13 Ramanujan-type supercongruences labeled (A.2)--(M.2). Using some combinatorial identities discovered by Sigma, we extend (A.2) and (H.2) to superc…
Congruences on sums of super Catalan numbers
Ji-Cai Liu
In this paper, we prove two congruences on the double sums of the super Catalan numbers (named by Gessel), which were recently conjectured by Apagodu.
Supercongruences for the th Apéry number
Ji-Cai Liu, Chen Wang
In this paper, we prove two conjectural supercongruences on the th Apéry number, which were recently proposed by Z.-H. Sun.
-Analogues of two Ramanujan-type formulas for
Victor J. W. Guo, Ji-Cai Liu
We give -analogues of the following two Ramanujan-type formulas for : \begin{align*} \sum_{k=0}^\infty (6k+1)\frac{(\frac{1}{2})_k^3}{k!^3 4^k} =\frac{4}π \quad\text{and}\q…