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A230821
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Decimal expansion of Product_{n>=3} cosh(Pi/n).
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2
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6, 1, 5, 0, 1, 8, 0, 2, 2, 0, 7, 9, 6, 8, 1, 7, 6, 9, 5, 2, 6, 8, 1, 7, 3, 9, 5, 8, 4, 8, 2, 1, 2, 3, 1, 8, 9, 8, 2, 6, 1, 6, 7, 8, 0, 6, 2, 0, 2, 8, 1, 2, 3, 6, 3, 2, 8, 2, 0, 8, 1, 5, 7, 2, 4, 4, 0, 2, 5, 7, 8, 8, 2, 8, 2, 2, 8, 7, 8, 3, 8, 9, 6, 3, 2, 4, 8, 9, 7, 6, 9, 7, 8, 4, 0, 5, 3, 2, 5, 9, 5, 7, 1, 4, 2
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OFFSET
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1,1
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LINKS
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FORMULA
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Equals exp(Sum_{k>=1} (2^(2*k)-1)*B(2*k)*(2*Pi)^(2*k)*(zeta(2*k)-1-1/2^(2*k))/(2*k*(2*k)!), where B(k) is the k-th Bernoulli number.
Equals exp(Sum_{k>=1} (-1)^(k+1)*(2^(2*k)-1)*zeta(2*k)*(zeta(2*k)-1-1/2^(2*k))/k). (End)
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EXAMPLE
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6.15018022079681769526817395848212318982616780620281236328208157244...
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MAPLE
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evalf(product(1/sech(Pi/k), k=3..infinity), 120) # Vaclav Kotesovec, Sep 20 2014
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MATHEMATICA
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(* RealDigits[ N[ Product[ Cosh[ Pi/n], {n, 3, Infinity}], 111]][[1]] *) [This approach turns out to give incorrect numerical results. - Vaclav Kotesovec, Sep 20 2014]
Block[{$MaxExtraPrecision = 1000}, Do[Print[N[1/Exp[Sum[(-1)^(n+1) * (2^(2*n)-1)/n * Zeta[2*n]*(Zeta[2*n] - 1 - 1/2^(2*n)), {n, 1, m}]], 110]], {m, 250, 300}]] (* Vaclav Kotesovec, Sep 20 2014 *)
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PROG
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(PARI) default(realprecision, 150); exp(sumpos(n=3, log(cosh(Pi/n)))) \\ Vaclav Kotesovec, Sep 20 2014
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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