let-consider-the-2pi-periodic-function-f-x-e-x-1-developp-f-at-fourier-serie-2-find-the-value-of-n-0-1-n-n-2-1-

Tinku Tara June 4, 2023 Integration 0 Comments

Question Number 33310 by abdo imad last updated on 14/Apr/18

let consider the 2π periodic?function f(x) =e^x 1) developp f at fourier serie 2) find the value of Σ_(n=0) ^∞ (((−1)^n )/(n^2 +1))

$${let}\:{consider}\:{the}\:\mathrm{2}\pi\:{periodic}?{function}\:\:{f}\left({x}\right)\:={e}^{{x}} \\ $$$$\left.\mathrm{1}\right)\:{developp}\:{f}\:{at}\:{fourier}\:{serie} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}^{\mathrm{2}} \:+\mathrm{1}} \\ $$

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