A family of q-supercongruences modulo the cube of a
cyclotomic polynomial
(7 pages)
Abstract.
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 previous 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.
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