Question Number 33295 by abdo imad last updated on 14/Apr/18
$${let}\:\:{f}\left({x}\right)=\:\left({x}+\mathrm{1}^{} \right)^{\mathrm{2}{n}} \:\:{e}^{−{nx}} \:\:{with}\:{n}\:{integr} \\ $$$$\left.\mathrm{1}\right)\:\:{calculste}\:\:{f}^{\left({p}\right)} \left({x}\right)\:\:{and}\:{f}^{\left({n}\right)} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{f}^{\left({p}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{3}\right)\:{developp}\:{f}\left({x}\right)\:{at}\:{integr}\:{serie}. \\ $$