Some parametric 𝑞-supercongruences from a summation of Gasper and Rahman

By employing a quadratic summation formula due to Gasper and Rahman [Basic hypergeometric series, 2nd ed, vol. 96, Cambridge University Press, Cambridge, 2004] and the creative microscoping method developed by Guo and Zudilin [Adv. Math. 346 (2019), pp. 329–358], we establish some new parametric q q -supercongruences, the corresponding supercongruences of which can be deemed the variants of Van Hamme’s (J.2) and (L.2) supercongruences. Moreover, we obtain three families of Ramanujan-type formulas on π π and propose a challenging conjecture.