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A242015
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Decimal expansion of the Euler-Kronecker constant (as named by P. Moree) for non-hypotenuse numbers.
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0
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4, 0, 9, 5, 0, 6, 9, 0, 3, 4, 1, 1, 8, 9, 5, 7, 6, 8, 2, 4, 5, 1, 1, 6, 3, 9, 5, 1, 8, 3, 7, 9, 7, 6, 3, 7, 0, 4, 3, 1, 9, 9, 5, 2, 9, 0, 9, 8, 4, 7, 1, 6, 6, 3, 2, 3, 4, 8, 9, 0, 9, 7, 6, 6, 8, 2, 7, 2, 5, 6, 9, 2, 7, 8, 0, 6, 3, 7, 6, 8, 8, 9, 2, 1, 2, 7, 2, 9, 8, 5, 0, 7, 0, 4, 4, 6, 0, 5, 2, 8, 7, 7, 5
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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 constants, p. 99.
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LINKS
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FORMULA
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EXAMPLE
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-0.40950690341189576824511639518379763704319952909847166323489...
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MATHEMATICA
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digits = 103; m0 = 5; dm = 5; beta[x_] := 1/4^x*(Zeta[x, 1/4] - Zeta[x, 3/4]); L = Pi^(3/2)/Gamma[3/4]^2*2^(1/2)/2; Clear[f]; f[m_] := f[m] = 1/2*(1 - Log[Pi*E^EulerGamma/(2*L)]) - 1/4*NSum[Zeta'[2^k]/Zeta[2^k] - beta'[2^k]/beta[2^k] + Log[2]/(2^(2^k) - 1), {k, 1, m}, WorkingPrecision -> digits + 10]; f[m0]; f[m = m0 + dm]; While[RealDigits[f[m], 10, digits] != RealDigits[f[m - dm], 10, digits], m = m + dm]; RealDigits[1 - 2*f[m] - EulerGamma + Log[Pi] - 4*Log[Gamma[3/4]], 10, digits] // First
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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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