let-give-f-x-e-x-cosx-and-2pi-periodic-1-developp-f-at-fourier-series-2-find-the-value-of-n-n-1-n-1-n-2-

Tinku Tara June 4, 2023 Integration 0 Comments

Question Number 28826 by abdo imad last updated on 30/Jan/18

let give f(x)= e^(−x) cosx and 2π periodic 1) developp f at fourier series 2) find the value of Σ_(n=−∞) ^(n=+∞) (((−1)^n )/(1+n^2 )) .

$${let}\:{give}\:{f}\left({x}\right)=\:{e}^{−{x}} \:{cosx}\:\:{and}\:\mathrm{2}\pi\:{periodic} \\ $$$$\left.\mathrm{1}\right)\:{developp}\:{f}\:{at}\:{fourier}\:{series} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\:\sum_{{n}=−\infty} ^{{n}=+\infty} \:\:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{\mathrm{1}+{n}^{\mathrm{2}} }\:. \\ $$

Facebook Tweet Pin

let-give-f-x-e-x-cosx-and-2pi-periodic-1-developp-f-at-fourier-series-2-find-the-value-of-n-n-1-n-1-n-2-

Leave a Reply Cancel reply