A new family of q-hypergeometric congruences from Andrews' multi-series transformation.

Abstract

We deduce a new family of q-hypergeometric congruences modulo the fourth power of a cyclotomic polynomial from George Andrews' multi-series extension of the Watson transformation. A Karlsson-Minton type summation for very-well-poised basic hypergeometric series due to George Gasper also plays an important role in our proof. We put forward two relevant conjectures on supercongruences and q-supercongruences for further study.