q-analogues of $π$-formulas due to Ramanujan and Guillera

The first known q-analogues for any of the $17$ formulas for 1π due to Ramanujan were introduced in 2018 by Guo and Liu (J. Difference Equ. Appl. 29:505-513, 2018), via the q-Wilf-Zeilberger method. Through a "normalization" method, which we refer to as EKHAD-normalization, based on the q-polynomial coefficients involved in first-order difference equations obtained from the q-version of Zeilberger's algorithm, we introduce q-WZ pairs that extend WZ pairs introduced by Guillera (Adv. in Appl. Math. 29:599-603, 2002) (Ramanujan J. 11:41-48, 2006). We apply our EKHAD-normalization method to prove four new q-analogues for three of Ramanujan's formulas for 1π along with q-analogues of Guillera's first two series for 1/π². Our normalization method does not seem to have been previously considered in any equivalent way in relation to q-series, and this is substantiated through our survey on previously known q-analogues of Ramanujan-type series for 1π and of Guillera's series for 1/π². We conclude by showing how our method can be adapted to further extend Guillera's WZ pairs by introducing hypergeometric expansions for 1/π².