Formelsammlung Mathematik: Unendliche Reihen: Mehrfachreihen

Zurück zu Unendliche Reihen

${\sum _{k_{1},...,k_{6}\in \mathbb {Z} }}'{\frac {(-1)^{k_{1}+...+k_{6}}}{(k_{1}^{2}+...+k_{6}^{2})^{s}}}=4\,\beta (s-2)\,\eta (s)-16\,\beta (s)\,\eta (s-2)\qquad {\text{Re}}(s)>1$

${\sum _{k_{1},...,k_{8}\in \mathbb {Z} }}'{\frac {(-1)^{k_{1}+...+k_{8}}}{(k_{1}^{2}+...+k_{8}^{2})^{s}}}=-16\,\zeta (s)\,\eta (s-3)\qquad {\text{Re}}(s)>1$