Some q-Supercongruences from a Quadratic Transformation by Rahman

被引：24

作者：

Liu, Yudong ^{[1
]}

Wang, Xiaoxia ^{[1
]}

机构：

[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China

来源：

RESULTS IN MATHEMATICS | 2022年 / 77卷 / 01期

关键词：

Basic hypergeometric series; supercongruences; q-congruences; cyclotomic polynomial; Rahman's transformation formula; Q-ANALOGS; CONGRUENCE;

D O I：

10.1007/s00025-021-01563-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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 Ranaanujan-type supercongruence, which has the same right-hand side as Van Hamme's (G.2) supercongruence for p 1 (mod 4). We also formulate some related challenging conjectures on supercongruences and q-supercongruences.

引用

页数：14

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