A family of q-hypergeometric congruences modulo
the fourth power of a cyclotomic polynomial
We prove a two-parameter family of q-hypergeometric
congruences modulo the fourth power of a cyclotomic polynomial.
Crucial ingredients in our proof are George Andrews' multiseries
extension of the Watson transformation, and a Karlsson--Minton type
summation for very-well-poised basic hypergeometric series due to
George Gasper. The new family of q-congruences is then used
to prove two conjectures posed earlier by the authors.
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