Question Number 28825 by abdo imad last updated on 30/Jan/18
$${let}\:{give}\:{f}\left({x}\right)=\:{e}^{−{x}} \:{cosx}\:{prove}\:{that} \\ $$$${f}\left({x}\right)=\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\:\:\frac{\left(\sqrt{\mathrm{2}}\right)^{{n}} }{{n}!}\:{cos}\left(\frac{\mathrm{3}{n}\pi}{\mathrm{4}}\right)\:{x}^{{n}} \:\:. \\ $$