Question Number 171094 by amin96 last updated on 07/Jun/22
$$\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}}: \\ $$$$\boldsymbol{\Omega}=\underset{\boldsymbol{\mathrm{n}}=\mathrm{0}} {\overset{\infty} {\sum}}\left(\frac{\left(\boldsymbol{\mathrm{n}}!\right)^{\mathrm{2}} }{\left(\mathrm{2}\boldsymbol{\mathrm{n}}\right)!}\right)^{\mathrm{2}} \frac{\mathrm{2}^{\mathrm{4}\boldsymbol{\mathrm{n}}} }{\left(\mathrm{2}\boldsymbol{\mathrm{n}}+\mathrm{1}\right)^{\mathrm{3}} }\overset{?} {=}\frac{\mathrm{7}}{\mathrm{2}}\boldsymbol{\zeta}\left(\mathrm{3}\right)−\pi\boldsymbol{\mathrm{G}} \\ $$$$\boldsymbol{\mathrm{G}}−\boldsymbol{\mathrm{Catalan}}'\boldsymbol{\mathrm{s}}\:\:\boldsymbol{\mathrm{constant}} \\ $$