DLMF:17.2.E42 (Q5332): Difference between revisions

Revision as of 14:51, 2 January 2020

No description defined

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

{\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}}}

0 references

DLMF:17.2.E42

0 references

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

C1.S2.SS1.m1amdec

0 references

@@ Property / Symbols used @@
+Q10754
@@ Property / Symbols used: Q10754 / rank @@
+Normal rank
@@ Property / Symbols used: Q10754 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}$ 
\binom{\NVar{m}}{\NVar{n}}
@@ Property / Symbols used: Q10754 / qualifier @@
+xml-id: C1.S2.SS1.m1amdec