Question and Answers Forum

All Questions      Topic List

None Questions

Previous in All Question      Next in All Question      

Previous in None      Next in None      

Question Number 112369 by mathdave last updated on 07/Sep/20

prove that   ∫_0 ^∞ (((tanhx)/x^3 )−((sech^2 x)/x^2 ))dx=(7/π^2 )ζ(3)  where ζ(3)=apery′s constant

$${prove}\:{that}\: \\ $$$$\int_{\mathrm{0}} ^{\infty} \left(\frac{\mathrm{tanh}{x}}{{x}^{\mathrm{3}} }−\frac{\mathrm{sech}^{\mathrm{2}} {x}}{{x}^{\mathrm{2}} }\right){dx}=\frac{\mathrm{7}}{\pi^{\mathrm{2}} }\zeta\left(\mathrm{3}\right) \\ $$$${where}\:\zeta\left(\mathrm{3}\right)={apery}'{s}\:{constant} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com