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prove-that-m-n-1-1-n-1-m-2-n-2-pi-2-24-piln-2-8-




Question Number 141134 by mnjuly1970 last updated on 16/May/21
          prove that::    Φ:=Σ_(m,n=1) ^∞ (((−1)^(n−1) )/(m^2 +n^2 ))= (π^2 /(24))+((πln(2))/8)
$$\:\:\:\:\: \\ $$$$\:\:\:{prove}\:{that}:: \\ $$$$\:\:\Phi:=\underset{{m},{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} }{{m}^{\mathrm{2}} +{n}^{\mathrm{2}} }=\:\frac{\pi^{\mathrm{2}} }{\mathrm{24}}+\frac{\pi{ln}\left(\mathrm{2}\right)}{\mathrm{8}} \\ $$$$ \\ $$
Answered by mindispower last updated on 17/May/21
tried but not solved
$${tried}\:{but}\:{not}\:{solved}\: \\ $$

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