A note on the \(q\)-derivative operator (Q1260891)

Defining \({\mathfrak D}_ q f(x)\), the \(q\)th derivative for \(x\neq 0\) as usual with \(f'(0)=0\) when \(x=0\), the authors prove \[ ({\mathfrak D}^ n_ q f)(0)=\lim_{x\to 0} {\mathfrak D}^ n_ q f(x)= {{f^{(n)}(0)} \over {n!}} {{(q;q)_ n} \over {(1-q)^ n}} \] for every \(f\), \(f^{(n)}(0)\) exists, \(x\in\mathbb{R}\); \(x\in\mathbb{C}\).