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A241005
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Decimal expansion of gamma', the analog of Euler's constant when 1/x is replaced by 1/(x*log(x)).
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1
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4, 2, 8, 1, 6, 5, 7, 2, 4, 8, 7, 1, 2, 3, 5, 0, 7, 5, 1, 9, 1, 4, 5, 8, 8, 0, 3, 8, 3, 2, 4, 8, 0, 0, 4, 4, 6, 1, 0, 7, 3, 6, 1, 4, 3, 0, 4, 5, 6, 9, 9, 7, 0, 5, 8, 4, 7, 8, 3, 4, 3, 8, 1, 3, 4, 4, 2, 5, 6, 2, 4, 3, 6, 4, 1, 3, 3, 4, 8, 2, 8, 1, 4, 7, 1, 5, 8, 9, 5, 4, 7, 7, 0, 6, 3, 5, 5, 6, 3
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refs;
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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 1.5.3 Generalized Euler Constants, p. 32.
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LINKS
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FORMULA
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lim_{m -> infinity} ( Sum_{n=2..m} 1/(n*log(n)) - log(log(m)/log(2)) ).
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EXAMPLE
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0.4281657248712350751914588...
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MATHEMATICA
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digits = 99; m0 = 10^digits; dm = 10^digits; Clear[g]; g[m_] := g[m] = NSum[1/(n*Log[n]) - (2*n*Log[Log[m]/Log[2]])/(-2 + m + m^2), {n, 2, m}, WorkingPrecision -> 2 digits, NSumTerms -> 1000, Method -> {"EulerMaclaurin", Method -> {"NIntegrate", "MaxRecursion" -> 30}}]; g[m = m0]; g[m = m0 + dm]; While[Print["m = ", m // N // ScientificForm, " ", RealDigits[g[m], 10, digits]]; RealDigits[g[m], 10, digits + 2] != RealDigits[g[m - dm], 10, digits + 2], m = m + dm]; RealDigits[g[m], 10, digits] // First (* updated Apr 19 2016 *)
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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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