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Question Number 124202 by mnjuly1970 last updated on 01/Dec/20

          :::  nice  calculus :::       prove  that :::    Σ_(m,n=1) ^∞ {(((−1)^(n+m) )/(n^2 +m^2 ))} =^(???) (π^2 /(12)) −(π/4)ln(2)

$$\:\:\:\:\:\:\:\:\:\::::\:\:{nice}\:\:{calculus}\:::: \\ $$$$\:\:\:\:\:{prove}\:\:{that}\:::: \\ $$$$ \\ $$$$\underset{{m},{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left\{\frac{\left(−\mathrm{1}\right)^{{n}+{m}} }{{n}^{\mathrm{2}} +{m}^{\mathrm{2}} }\right\}\:\overset{???} {=}\frac{\pi^{\mathrm{2}} }{\mathrm{12}}\:−\frac{\pi}{\mathrm{4}}{ln}\left(\mathrm{2}\right) \\ $$

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