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


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Question Number 124202 by mnjuly1970 last updated on 01/Dec/20
$::: nice calculus ::: prove that ::: Σ_(m,n=1) ^∞ {(((−1)^(n+m) )/(n^2 +m^2 ))} =^(???) (π^2 /(12)) −(π/4)ln(2)$
$::: n i c e c a l c u l u s :::$ $p r o v e t h a t :::$ $\underset{m, n = 1}{\sum^{\infty}} {\frac{{(- 1)}^{n + m}}{n^{2} + m^{2}}} \overset{? ? ?}{=} \frac{π^{2}}{12} - \frac{π}{4} l n (2)$
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