Result: Integral representations of multiple basic hypergeometric functions

By using the well-known fractional \(q\)-derivative operator, defined by \[ D^ \alpha_{q,x}f(x)=x^{-\alpha}(1-q)^{-\alpha}\sum_{n\geq 0}{(q^{-\alpha};q)_ n\over (q;q)_ n}f(xq^ n) \] the authors derive certain integral representations for the multiple basic hypergeometric functions. The results are too lengthy to be mentioned here. There are some misprints in the paper. For example the correct form of (1.4) is \([x-y]_ u=x^ u\prod^ \infty_{n=0}(1-yq^ n/x)/(1-yq^{u+n}/x)\).