Combinatorics

Discrete mathematics

Hypergeometric function of a matrix argument

Hypergeometric function

Pure mathematics

Mathematics

Cube (algebra)

Modulo

Algebra over a field

Generalized hypergeometric function

Mathematical analysis

Hypergeometric identity

Conjecture

Cyclotomic polynomial

Polynomial

Arithmetic

Bulletin of the Australian Mathematical Society

We establish a family of q -supercongruences modulo the cube of a cyclotomic polynomial for truncated basic hypergeometric series. This confirms a weaker form of a conjecture of the present authors. Our proof employs a very-well-poised Karlsson–Minton type summation due to Gasper, together with the ‘creative microscoping’ method introduced by the first author in recent joint work with Zudilin.

A FAMILY OF -SUPERCONGRUENCES MODULO THE CUBE OF A CYCLOTOMIC POLYNOMIAL