Formelsammlung Mathematik: Unendliche Reihen: Doppelreihen

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$\sum _{k,j=1}^{\mathrm{\infty }}\frac{1}{kj(k+j{)}^2}=\frac{{\pi }^4}{180}$

Blender3D: Vorlage:Klappbox

$\sum _{k,j=1}^{\mathrm{\infty }}\frac{1}{(k\pi {)}^{2n}(j\pi {)}^{2n}(k\pi +j\pi {)}^{2n}}=\frac{(-1{)}^{n-1}}{6}\underset{0}{\overset{1}{\int }}{\left(\frac{2^{2n}{B}_{2n}(x)}{(2n)!}\right)}^{3}dx\in \mathbb{Q}$

Blender3D: Vorlage:Klappbox

$\sum _{n,m\in \mathbb{Z}}\text{'}\frac{1}{(n^2+m^2{)}^s}=4\beta (s)\zeta (s)\text{Re}(s)>1$

Blender3D: Vorlage:Klappbox

$\sum _{n,m\in \mathbb{Z}}\text{'}\frac{(-1{)}^{n+m}}{(n^2+m^2{)}^s}=-4\beta (s)\eta (s)\text{Re}(s)>1$