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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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