Parametric Generalizations of Two Ramanujan-type Supercongruences

We prove that, for any odd prime [Formula: see text] and [Formula: see text], [Formula: see text] where [Formula: see text] and [Formula: see text] for [Formula: see text]. When [Formula: see text], this supercongruence reduces to a result of Guillera and Zudilin in 2012. We shall prove this result by building a [Formula: see text]-analogue of it. The main ingredients of the proof include the method of “creative microscoping” devised by Guo and Zudilin, a quadratic transformation of Rahman, a quadratic transformation of Gasper and Rahman, and Jackson’s [Formula: see text] summation. We also give a similar generalization of a supercongruence of Guo and Zudilin along with its [Formula: see text]-analogue.