New q-supercongruences from the Bailey transformation

TL;DR

This paper introduces new q-supercongruences, including q-analogues of Ramanujan-type supercongruences, achieved through Bailey transformation and creative microscoping methods, expanding the understanding of q-series congruences.

Contribution

The paper presents novel q-supercongruences derived from Bailey transformation and creative microscoping, extending Ramanujan-type supercongruences in the q-series context.

Findings

Established new q-supercongruences

Derived q-analogues of Ramanujan-type supercongruences

Applied Bailey transformation and creative microscoping methods

Abstract

Inspired by the recent work of Guo, we establish some new q-supercongruences including q-analogues of some Ramannujan-type supercongruences, by using the Bailey transformation formula and the `creative microscoping' method recently introduced by Guo and Zudilin.