Paper Info
Title
q -Supercongruences from Gasper and Rahman's summation formula.
Abstract
In 2017, He [Proc. Amer. Math. Soc. 145 (2017), 501--508] established two spuercongruences on truncated hypergeometric series and further proposed two related conjectures. Subsequently, Liu [Results Math. 72 (2017), 2057--2066] extended He's formulas and confirmed the second conjecture. However, the first conjecture is still open up to now. With the help of the creative microscoping method and the Chinese remainder theorem for coprime polynomials, we derive several $q$-supercongruences modulo the fourth and fifth powers of a cyclotomic polynomial from Gasper and Rahman's summation formula for basic hypergeometric series. As conclusions, He's first conjecture is confirmed and a more general form of He's second conjecture is proved.
Year
DOI
Venue
2022
10.1016/j.aam.2022.102376
Advances in Applied Mathematics
DocType
Volume
ISSN
Journal
139
0196-8858
Citations 
PageRank 
References 
0
0.34
0
Authors
1
Name
Order
Citations
PageRank
Chuanan Wei1207.98