𝑞-supercongruences for double series with parameters

In this paper, we establish two q q -supercongruences for double series with parameters. When the parameters are specified, they reduce to two known results and can produce a lot of new supercongruences including the following two ones: a m p ; ∑ k = 0 ( p − 1 ) / 2 ( 4 k + 1 ) ( 1 2 ) k 3 ( 1 ) k 3 ∑ j = 1 2 k ( − 1 ) k + j + 1 j 2 ≡ p ∑ k = 0 ( p − 1 ) / 2 ( 1 2 ) k 2 <mml:mo stretchy=