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determinant-prove-that-n-1-H-n-H-n-2-n-3-n-1-H-n-H-n-3-n-2-21-8-6-2-3-by-Math-Amin-11-fb-96-




Question Number 154544 by amin96 last updated on 19/Sep/21
 determinant (((prove that)),((Σ_(n=1) ^∞ ((H_n H_n ^((2)) )/n^3 )+Σ_(n=1) ^∞ ((H_n H_n ^((3)) )/n^2 )=((21)/8)𝛇(6)+𝛇^2 (3))))  by Math.Amin  11.fb.96
$$\begin{array}{|c|c|}{\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}}}\\{\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\boldsymbol{\mathrm{H}}_{\boldsymbol{\mathrm{n}}} \boldsymbol{\mathrm{H}}_{\boldsymbol{\mathrm{n}}} ^{\left(\mathrm{2}\right)} }{\boldsymbol{\mathrm{n}}^{\mathrm{3}} }+\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\boldsymbol{\mathrm{H}}_{\boldsymbol{\mathrm{n}}} \boldsymbol{\mathrm{H}}_{\boldsymbol{\mathrm{n}}} ^{\left(\mathrm{3}\right)} }{\boldsymbol{\mathrm{n}}^{\mathrm{2}} }=\frac{\mathrm{21}}{\mathrm{8}}\boldsymbol{\zeta}\left(\mathrm{6}\right)+\boldsymbol{\zeta}^{\mathrm{2}} \left(\mathrm{3}\right)}\\\hline\end{array} \\ $$$${by}\:{Math}.{Amin}\:\:\mathrm{11}.{fb}.\mathrm{96} \\ $$

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