A228725 revision #53
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A228725
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Decimal expansion of the generalized Euler constant gamma(1,2).
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19
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6, 3, 5, 1, 8, 1, 4, 2, 2, 7, 3, 0, 7, 3, 9, 0, 8, 5, 0, 1, 1, 8, 7, 2, 1, 0, 5, 7, 7, 0, 2, 8, 9, 4, 9, 9, 5, 5, 8, 8, 2, 9, 7, 3, 5, 1, 5, 0, 0, 8, 9, 4, 2, 6, 4, 6, 3, 2, 2, 3, 6, 2, 2, 1, 8, 9, 1, 3, 0, 6, 7, 4, 3, 7, 3, 6, 7, 9, 6, 9, 3, 2, 7, 1
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OFFSET
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0,1
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COMMENTS
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LINKS
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FORMULA
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Equals lim_{x -> oo} (Sum_{0<n<=x, n odd} 1/n - log(x)/2).
Equals -Integral_{x=0..1} log(log(1/x))*x dx.
Equals -Integral_{x=0..oo} exp(-2*x)*log(x) dx. (End)
Equals Integral_{x=0..1, y=0..1} log(-log(x*y))*x*y/log(x*y) dx dy. (Apply Theorem 1 or Theorem 2 of Glasser (2019) to one of Amiram Eldar's integrals.) - Petros Hadjicostas, Jun 30 2020
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EXAMPLE
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.63518142273073908501187210577028949955882973515008942646322...
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MAPLE
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(gamma+log(2))/2 ; evalf(%) ;
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MATHEMATICA
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RealDigits[(EulerGamma+Log[2])/2, 10, 120][[1]] (* Harvey P. Dale, Dec 26 2013 *)
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PROG
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(Magma) SetDefaultRealField(RealField(100)); R:= RealField();
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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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