An extension of a supercongruence of Long and Ramakrishna
From MaRDI portal
Publication:5060359
DOI10.1090/proc/16179OpenAlexW3115765469MaRDI QIDQ5060359
Michael J. Schlosser, Victor J. W. Guo, Ji-Cai Liu
Publication date: 10 January 2023
Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2012.13672
hypergeometric seriessupercongruences\(p\)-adic gamma functionWhipple's transformationKarlsson-Minton's summation
Binomial coefficients; factorials; (q)-identities (11B65) Congruences; primitive roots; residue systems (11A07) Generalized hypergeometric series, ({}_pF_q) (33C20)
Related Items (3)
Some congruences that extend Van Hamme's (D.2) supercongruence ⋮ Two \(q\)-operational equations and Hahn polynomials ⋮ \(q\)-supercongruences from Jackson's \({}_8 \phi_7\) summation and Watson's \({}_8 \phi_7\) transformation
Cites Work
- Unnamed Item
- Unnamed Item
- A \(p\)-adic supercongruence for truncated hypergeometric series \({}_7F_6\)
- On supercongruences for truncated sums of squares of basic hypergeometric series
- Some supercongruences occurring in truncated hypergeometric series
- A \(p\)-adic analogue of a formula of Ramanujan
- On Van Hamme's (A.2) and (H.2) supercongruences
- A \(q\)-microscope for supercongruences
- Supercongruences arising from transformations of hypergeometric series
- Proof of a \(q\)-supercongruence conjectured by Guo and Schlosser
- Supercongruences for sums involving fourth power of some rising factorials
- A family of \(q\)-hypergeometric congruences modulo the fourth power of a cyclotomic polynomial
- Congruences on sums of \(q\)-binomial coefficients
- Some new \(q\)-congruences for truncated basic hypergeometric series
- A $p$-adic supercongruence conjecture of van Hamme
- A FAMILY OF -SUPERCONGRUENCES MODULO THE CUBE OF A CYCLOTOMIC POLYNOMIAL
- Some congruences related to a congruence of Van Hamme
- Number Theory
This page was built for publication: An extension of a supercongruence of Long and Ramakrishna