259 citations
- Radboud University NijmegenNL5 papers
- Beijing Computational Science Research CenterCN4 papers
- Chinese Academy of SciencesCN4 papers
- East China Normal UniversityCN4 papers
- Nanjing UniversityCN4 papers
- Nanjing Normal UniversityCN3 papers
- Singapore University of Technology and DesignSG3 papers
- Tongji UniversityCN3 papers
- University of ViennaAT3 papers
- Wuhan Institute of Physics and MathematicsCN3 papers
- Argonne National LaboratoryUS2 papers
- Centre National de la Recherche ScientifiqueFR2 papers
13 papers · 1 filter
Some congruences related to a congruence of Van Hamme
Victor J. W. Guo, Ji-Cai Liu
We establish some supercongruences related to a supercongruence of Van Hamme, such as \begin{align*} \sum_{k=0}^{(p+1)/2} (-1)^k (4k-1)\frac{(-\frac{1}{2})_k^3}{k!^3} &\equiv p(-1)…
Proofs of two conjectures on Catalan triangle numbers
Victor J. W. Guo, Xiuguo Lian
We prove two conjectures on sums of products of Catalan triangle numbers, which were originally conjectured by Miana, Ohtsuka, and Romero [Discrete Math. 340 (2017), 2388--2397]. T…
A recursive algorithm for trees and forests
Song Guo, Victor J. W. Guo
Trees or rooted trees have been generously studied in the literature. A forest is a set of trees or rooted trees. Here we give recurrence relations between the number of some kind…
Factors of sums involving -binomial coefficients and powers of -integers
Victor J. W. Guo, Su-Dan Wang
We show that, for all positive integers , , and any non-negative integers and with , the expression $$ \frac{1}{[n_1]}{n_1+n_{m…
A -Clausen-Orr type formula and its applications
Hong-Fang Guo, Victor J. W. Guo, Jiang Zeng
We show that certain terminating series can be factorized into a product of two series. As applications we prove a summation formula for a product of two -…
Basic and bibasic identities related to divisor functions
Victor J. W. Guo, Jiang Zeng
Using basic hypergeometric functions and partial fraction decomposition we give a new kind of generalization of identities due to Uchimura, Dilcher, Van Hamme, Prodinger, and Chen-…