Due to specific knowledge, I know that this is a constant which has a very nice closed form expression (probably short and in terms of square roots, rationals, and $\pi$). However, the Inverse Symbolic Calculator and I can't find it. What is $0.25801227546$ a very good approximation to?
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3Can you give any further context on this 'specific knowledge'? – orlp Dec 08 '19 at 00:57
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4Wolfram Alpha thinks that it could be an approximation of $8/\pi^3$. – conditionalMethod Dec 08 '19 at 00:58
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@orlp It was the value of a summation that is supposed to telescope. I haven't made it telescope yet. – Display name Dec 08 '19 at 01:51
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I used the program $\texttt{ries}$ and it found a close match:
> ries 0.25801227546
Your target value: T = 0.25801227546 mrob.com/ries
cospi(x) = ln(2) for x = T - 0.00178869 {54}
e^(1/x) = 7^2 for x = T - 0.0010631 {62}
3"/x = 2/pi for x = T + 5.59597e-12 {69}
(for more results, use the option '-l3')
ln(x) = natural logarithm or log base e cospi(X) = cos(pi * x)
A"/B = Ath root of B pi = 3.14159...
which gives the value $(2/\pi)^3$.
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