Further $q$-supercongruences from a transformation of Rahman
Victor J. W. Guo
TL;DR
This paper uses Rahman's quadratic transformation and creative microscoping to establish new $q$-supercongruences for hypergeometric series, confirming recent conjectures and proposing new ones.
Contribution
It introduces novel $q$-supercongruences derived from Rahman's transformation, confirming two recent conjectures and suggesting further related conjectures.
Findings
Confirmed two recent conjectures of Liu and Wang
Derived new $q$-supercongruences for hypergeometric series
Proposed several related conjectures on supercongruences
Abstract
Employing a quadratic transformation formula of Rahman and the method of `creative microscoping' (introduced by the author and Zudilin in 2019), we provide some new -supercongruences for truncated basic hypergeometric series. In particular, we confirm two recent conjectures of Liu and Wang. We also propose some related conjectures on supercongruences and -supercongruences.
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Taxonomy
TopicsAdvanced Mathematical Identities