Question Number 119323 by mnjuly1970 last updated on 23/Oct/20
Commented by Dwaipayan Shikari last updated on 23/Oct/20
$${What}\:{is}\:\eta\left(\mathrm{2}{n}+\mathrm{1}\right)? \\ $$
Commented by mnjuly1970 last updated on 23/Oct/20
$$\:\:{drichlet}\:\:{eta}\:{function} \\ $$$$\:\:\:\:\:\:\eta\left({s}\right)=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} }{{n}^{{s}} } \\ $$$$\:\:\:\:\:{example}:\:\:\eta\left(\mathrm{2}\right)=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} }{{n}^{\mathrm{2}} }\:=\frac{\mathrm{1}}{\mathrm{2}}\zeta\left(\mathrm{2}\right)=\frac{\pi^{\mathrm{2}} }{\mathrm{12}}\:… \\ $$
Commented by Dwaipayan Shikari last updated on 23/Oct/20
$$\left.{As}\:{a}\:{student}\:,\:{I}\:{am}\:{glad}\:{to}\:{learn}\:{from}\:{you}\:{sir}!\:\::\right) \\ $$
Commented by mnjuly1970 last updated on 23/Oct/20
$$\:\:\:{thank}\:{you}\:{so}\:{much}\:. \\ $$$$\:\:\:{to}\:{me}\:{you}\:{are}\:{very}\:{poweful} \\ $$$$\:{in}\:{mathematics}.{good}\:{for}\:{you}\:{and}\: \\ $$$${good}\:{luck}\:{mr}\:{Dwaipayan}… \\ $$$$\: \\ $$
Answered by mindispower last updated on 23/Oct/20
$${nice} \\ $$