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"published": "2024-10-04T11:27:31Z",
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"content": "<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>",
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"en": "<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>"
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"updated": "2024-10-04T11:30:44Z",
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