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A243377
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Decimal expansion of a constant related to the asymptotic evaluation of Product_{p prime congruent to 1 modulo 4} (1 + 1/p).
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0
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7, 3, 2, 6, 4, 9, 8, 1, 9, 2, 8, 3, 8, 3, 2, 6, 1, 3, 6, 2, 0, 3, 0, 5, 8, 2, 3, 1, 1, 7, 6, 8, 3, 6, 8, 7, 3, 6, 3, 1, 6, 9, 9, 4, 4, 1, 9, 9, 4, 6, 3, 2, 9, 3, 4, 5, 0, 6, 0, 7, 7, 7, 2, 9, 6, 3, 8, 3, 4, 3, 1, 9, 3, 3, 1, 8, 7, 7, 1, 9, 0, 6, 4, 0, 4, 9, 1, 5, 5, 2, 9, 2, 7, 7, 9, 6, 8, 9, 1, 4, 6, 7, 6
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OFFSET
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0,1
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.3 Landau-Ramanujan constant, p. 101.
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LINKS
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FORMULA
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Equals (4/Pi^(3/2))*exp(gamma/2)*K, where gamma is the Euler-Mascheroni constant and K the Landau-Ramanujan constant.
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EXAMPLE
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0.732649819283832613620305823117683687363...
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MATHEMATICA
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digits = 103; LandauRamanujanK = 1/Sqrt[2]*NProduct[((1 - 2^(-2^n))*Zeta[2^n]/DirichletBeta[2^n])^(1/2^(n + 1)), {n, 1, 24}, WorkingPrecision -> digits + 5]; 4/Pi^(3/2)*Exp[EulerGamma/2]*LandauRamanujanK // RealDigits[#, 10, digits] & // First (* updated Mar 14 2018 *)
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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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