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please-a-generall-Form-for-C-n-C-n-4-pi-2-k-1-n-1-k-1-2k-2n-2k-




Question Number 136325 by frc2crc last updated on 20/Mar/21
please a generall Form for C(n)  C(n)=(4/π^2 )Σ_(k=1) ^n (−1)^(k−1) ζ(2k)ζ(2n−2k)
$${please}\:{a}\:{generall}\:{Form}\:{for}\:{C}\left({n}\right) \\ $$$${C}\left({n}\right)=\frac{\mathrm{4}}{\pi^{\mathrm{2}} }\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\left(−\mathrm{1}\right)^{{k}−\mathrm{1}} \zeta\left(\mathrm{2}{k}\right)\zeta\left(\mathrm{2}{n}−\mathrm{2}{k}\right) \\ $$
Commented by Dwaipayan Shikari last updated on 20/Mar/21
C(1)→Diverges  C(2)→Diverges  C(3)→Diverges   ..  No such General form..
$${C}\left(\mathrm{1}\right)\rightarrow{Diverges} \\ $$$${C}\left(\mathrm{2}\right)\rightarrow{Diverges} \\ $$$${C}\left(\mathrm{3}\right)\rightarrow{Diverges}\: \\ $$$$.. \\ $$$${No}\:{such}\:{General}\:{form}.. \\ $$

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