We give q-analogues of three Ramanujan-type series for \(1/\pi \) from q-analogues of ordinary WZ pairs. The first one is a new q-analogue of the following Ramanujan’s formula for \(1/\pi \):$$\begin{aligned} \sum _{n=0}^\infty \frac{6n+1}{256^n}{2n\atopwithdelims ()n}^3=\frac{4}{\pi }, \end{aligned}$$of which another q-analogue was given by the author and Liu early and reproved by different authors. We also present a WZ proof of a q-analogue of Bauer’s (Ramanujan-type) formula and discuss some related congruences and q-congruences.

中文翻译：

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q-三种Ramanujan型公式的类似物，分别为$$ 1 / \ pi $$ 1 /π

我们给q三拉马努金型系列-analogues为\（1 / \ PI \）从q普通WZ对-analogues。第一个是以下Ramanujan的\（1 / \ pi \）公式的新q模拟：$$ \ begin {aligned} \ sum _ {n = 0} ^ \ infty \ frac {6n + 1} { 256 ^ n} {2n \ atopwithdelims（）n} ^ 3 = \ frac {4} {\ pi}，\ end {aligned} $$，其中另一个q模拟是由作者和Liu提早给出的，并得到了不同的证明。作者。我们还提出了鲍尔（Ramanujan型）公式的q模拟的WZ证明，并讨论了一些相关的等式和q-等式。