DLMF:17.2.E42 (Q5332)

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Language	Label	Description	Also known as
English	DLMF:17.2.E42	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle f^{[n]}(z)=\mathcal{D}_{q}^{n}f(z)=\begin{cases}z% ^{-n}(1-q)^{-n}\sum_{j=0}^{n}q^{-nj+\genfrac{(}{)}{0.0pt}{}{j+1}{2}}(-1)^{j}% \genfrac{[}{]}{0.0pt}{}{n}{j}_{q}f(zq^{j}),&z\neq 0,\\ \dfrac{f^{(n)}(0)\left(q;q\right)_{n}}{n!(1-q)^{n}},&z=0.\end{cases}}}

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DLMF:17.2.E42

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Defining formula

{\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}

C1.S2.SS1.m1amdec

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