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A373208
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Decimal expansion of Product_{k>=1} f(2*k)^2/(f(2*k-1) * f(2*k+1)), where f(k) = k^(1/k^2).
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1
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1, 2, 2, 4, 6, 2, 3, 1, 4, 0, 5, 8, 5, 1, 1, 1, 1, 4, 5, 5, 9, 5, 2, 5, 7, 0, 4, 5, 1, 6, 2, 1, 5, 8, 9, 4, 7, 2, 0, 1, 0, 1, 8, 4, 4, 8, 3, 2, 0, 3, 2, 1, 5, 1, 9, 8, 3, 1, 0, 8, 8, 2, 7, 8, 9, 9, 0, 7, 0, 6, 9, 3, 3, 4, 7, 9, 0, 1, 1, 6, 5, 5, 6, 5, 4, 0, 0, 4, 3, 2, 5, 0, 6, 1, 3, 1, 8, 4, 4, 2, 2, 7, 3, 8, 0
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OFFSET
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1,2
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LINKS
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FORMULA
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Equals exp(2*eta'(2)) = exp(2*A210593), where eta is the Dirichlet eta function.
Equals (4*Pi*exp(gamma)/A^12)^zeta(2), where gamma is Euler's constant (A001620) and A is the Glaisher-Kinkelin constant (A074962).
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EXAMPLE
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(2^(1/2^2)/1^1^2) * (2^(1/2^2)/3^(1/3^2)) * (4^(1/4^2)/3^(1/3^2)) * (4^(1/4^2)/5^(1/5^2)) * ...
1.22462314058511114559525704516215894720101844832032...
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MATHEMATICA
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RealDigits[(4 * Pi * Exp[EulerGamma] / Glaisher^12)^Zeta[2], 10, 120][[1]]
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PROG
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(PARI) (4 * Pi * exp(Euler - 1 + 12*zeta'(-1)))^zeta(2)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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