A family of <inline-formula><tex-math id="M1">$ q $</tex-math></inline-formula>-congruences modulo the square of a cyclotomic polynomial
A family of <inline-formula><tex-math id="M1">$ q $</tex-math></inline-formula>-congruences modulo the square of a cyclotomic polynomial
<p style='text-indent:20px;'>Using Watson's terminating <inline-formula><tex-math id="M2">$ _8\phi_7 $</tex-math></inline-formula> transformation formula, we prove a family of <inline-formula><tex-math id="M3">$ q $</tex-math></inline-formula>-congruences modulo the square of a cyclotomic polynomial, which were originally conjectured by the author and Zudilin [J. Math. Anal. Appl. 475 (2019), 1636-646]. As an application, we deduce two supercongruences modulo …