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Double q-analog of Pochhammer

Has the function $$(z;q_1,q_2)_\infty := \prod_{n_1,n_2=0}^\infty (1-z \, q_1^{n_1} q_2^{n_2}), \quad |q_1|,|q_2|<1$$ been studied in the math literature? For example, does it obey any difference ...
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