Q-Beta function

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$$B_q(a,b) = \dfrac{\Gamma_q(a)\Gamma_q(b)}{\Gamma_q(a+b)}$$

$$B_q(a,b) = \displaystyle\int_0^1 \dfrac{t^{a-1}(tq;q)_{\infty}}{(tq^b;q)_{\infty}} d_q t$$

References[edit]

DLMF entry on $q$-Gamma and $q$-Beta functions