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A081855
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Decimal expansion of Gamma''(1).
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4
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1, 9, 7, 8, 1, 1, 1, 9, 9, 0, 6, 5, 5, 9, 4, 5, 1, 1, 0, 7, 9, 0, 7, 9, 1, 3, 0, 3, 0, 0, 1, 2, 6, 9, 4, 1, 5, 8, 7, 8, 3, 6, 7, 0, 4, 1, 4, 5, 6, 4, 2, 8, 1, 8, 0, 8, 8, 6, 3, 9, 1, 5, 6, 7, 3, 7, 2, 2, 7, 3, 2, 6, 4, 0, 9, 8, 9, 5, 7, 5, 4, 3, 4, 9, 4, 8, 9, 2, 1, 6, 9, 2, 5, 1, 4, 7, 4, 6, 8, 2, 6, 0, 7, 0, 4
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OFFSET
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1,2
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COMMENTS
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Also the decimal expansion of the Integral_{x>=0} exp(-x)*(log(x))^2 dx. - Robert G. Wilson v, Aug 18 2017
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REFERENCES
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Bruce C. Berndt, Ramanujan's notebooks Part II, Springer, p. 179
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LINKS
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FORMULA
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The second derivative of Gamma(x) at x=1 is Gamma^2+zeta(2) = 1.97811199... where Gamma is the Euler constant and zeta(2) = Pi^2/6.
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EXAMPLE
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1.978111990655945110790791303001269415878367... [corrected by Georg Fischer, Jul 29 2021]
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MATHEMATICA
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RealDigits[ Integrate[ Exp[-x]*Log[x]^2, {x, 0, Infinity}], 10, 111][[1]] (* Robert G. Wilson v, Aug 18 2017 *)
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PROG
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(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); L:=RiemannZeta(); EulerGamma(R)^2 + Evaluate(L, 2); // G. C. Greubel, Aug 29 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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