Pustam | पुस्तम | পুস্তম🇳🇵A lattice sum with a surprising closed form:
\[\Large\displaystyle\sum_{\substack{(m,n)\in\mathbb Z^2\\(m,n)\neq0}}\dfrac{1}{(m+ni)^4}=\dfrac{\varpi^4}{15}=\dfrac{\Gamma^8\left(\frac14\right)}{960\pi^2}\]
#LatticeSum #ClosedForm #LemniscateConstant #Series #Sum #GammaFunction #Pi
\[\Large\displaystyle\sum_{\substack{(m,n)\in\mathbb Z^2\\(m,n)\neq0}}\dfrac{1}{(m+ni)^4}=\dfrac{\varpi^4}{15}=\dfrac{\Gamma^8\left(\frac14\right)}{960\pi^2}\]
#LatticeSum #ClosedForm #LemniscateConstant #Series #Sum #GammaFunction #Pi