Question Number 91195 by student work last updated on 28/Apr/20
$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{duble}\:\mathrm{fictorial}\:\mathrm{furmolla}? \\ $$
Answered by MJS last updated on 28/Apr/20
$${n}!!=\begin{cases}{\underset{{k}=\mathrm{1}} {\overset{\frac{{n}}{\mathrm{2}}} {\prod}}\left(\mathrm{2}{k}\right)\:\mathrm{for}\:\mathrm{even}\:{n}}\\{\underset{{k}=\mathrm{1}} {\overset{\frac{{n}+\mathrm{1}}{\mathrm{2}}} {\prod}}\left(\mathrm{2}{k}−\mathrm{1}\right)\:\mathrm{for}\:\mathrm{uneven}\:{n}}\end{cases} \\ $$$$\mathrm{0}!!=\mathrm{1} \\ $$$$\mathrm{for}\:{n}\geqslant\mathrm{1}:\:{n}!={n}!!\left({n}−\mathrm{1}\right)!! \\ $$