Pustam | पुस्तम | পুস্তম🇳🇵<p>Let \(\varpi=\dfrac{\Gamma^2\left(\frac14\right)}{2\sqrt{2\pi}}=2.62205755\ldots\) be the lemniscate constant. Then,<br />\[\Large\displaystyle\sum_{n=1}^\infty\dfrac{1}{\sinh^4(\pi n)}=\dfrac{\varpi^4}{30\pi^4}+\dfrac{1}{3\pi}-\dfrac{11}{90}\]</p><p><a href="https://mathstodon.xyz/tags/Series" class="mention hashtag" rel="tag">#<span>Series</span></a> <a href="https://mathstodon.xyz/tags/Sum" class="mention hashtag" rel="tag">#<span>Sum</span></a> <a href="https://mathstodon.xyz/tags/InfiniteSum" class="mention hashtag" rel="tag">#<span>InfiniteSum</span></a> <a href="https://mathstodon.xyz/tags/LemniscateConstant" class="mention hashtag" rel="tag">#<span>LemniscateConstant</span></a> <a href="https://mathstodon.xyz/tags/GammaFunction" class="mention hashtag" rel="tag">#<span>GammaFunction</span></a> <a href="https://mathstodon.xyz/tags/Lemniscate" class="mention hashtag" rel="tag">#<span>Lemniscate</span></a> <a href="https://mathstodon.xyz/tags/LemniscateOfBernoulli" class="mention hashtag" rel="tag">#<span>LemniscateOfBernoulli</span></a> <a href="https://mathstodon.xyz/tags/Bernoulli" class="mention hashtag" rel="tag">#<span>Bernoulli</span></a> <a href="https://mathstodon.xyz/tags/Math" class="mention hashtag" rel="tag">#<span>Math</span></a> <a href="https://mathstodon.xyz/tags/Maths" class="mention hashtag" rel="tag">#<span>Maths</span></a> <a href="https://mathstodon.xyz/tags/InfiniteSeries" class="mention hashtag" rel="tag">#<span>InfiniteSeries</span></a> <a href="https://mathstodon.xyz/tags/HyperbolicSines" class="mention hashtag" rel="tag">#<span>HyperbolicSines</span></a></p>