let-give-x-x-2pi-periodique-even-developp-f-at-fourier-series-then-find-the-value-of-n-1-1-n-n-2-and-n-0-1-2n-1-2-

Tinku Tara June 4, 2023 Integration 0 Comments

Question Number 28833 by abdo imad last updated on 30/Jan/18

let give ϕ(x) =x ,ϕ 2π periodique even developp f at fourier series then find the value of Σ_(n=1) ^∞ (((−1)^n )/n^2 ) and Σ_(n=0) ^∞ (1/((2n+1)^2 )) .

$${let}\:{give}\:\varphi\left({x}\right)\:={x}\:,\varphi\:\mathrm{2}\pi\:{periodique}\:{even} \\ $$$${developp}\:{f}\:{at}\:{fourier}\:{series}\:{then}\:{find}\:{the}\:{value}\:{of} \\ $$$$\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}^{\mathrm{2}} }\:{and}\:\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{1}}{\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{2}} }\:. \\ $$

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let-give-x-x-2pi-periodique-even-developp-f-at-fourier-series-then-find-the-value-of-n-1-1-n-n-2-and-n-0-1-2n-1-2-

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