Some q-Supercongruences from a Quadratic Transformation by Rahman

被引：0
作者：
Yudong Liu
Xiaoxia Wang
机构：
[1] Shanghai University,Department of Mathematics
来源：
Results in Mathematics | 2022年 / 77卷
关键词：
Basic hypergeometric series; supercongruences; -congruences; cyclotomic polynomial; Rahman’s transformation formula; Primary 33D15; Secondary 11A07; 11B65;
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摘要：
Inspired by the recent work on q-congruences and a quadratic transformation formula of Rahman, we provide some new q-supercongruences. By taking parameters specialization in one of our results, we obtain a new Ramanujan-type supercongruence, which has the same right-hand side as Van Hamme’s (G.2) supercongruence for p≡1(mod4)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p\equiv 1 \pmod 4$$\end{document}. We also formulate some related challenging conjectures on supercongruences and q-supercongruences.
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