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A247017
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Decimal expansion of integral_{0..infinity} exp(-x^2)*log(x) dx.
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1
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8, 7, 0, 0, 5, 7, 7, 2, 6, 7, 2, 8, 3, 1, 5, 5, 0, 6, 7, 3, 4, 6, 4, 8, 7, 9, 9, 5, 3, 6, 0, 8, 7, 4, 3, 7, 5, 0, 8, 1, 0, 7, 3, 3, 3, 6, 2, 5, 9, 4, 0, 0, 5, 3, 7, 8, 8, 5, 8, 3, 3, 8, 5, 1, 9, 6, 5, 2, 5, 8, 4, 2, 7, 1, 4, 4, 2, 9, 5, 4, 0, 0, 8, 3, 7, 2, 1, 9, 5, 0, 7, 8, 7, 7, 1, 9, 4, 2, 9, 6, 9, 1
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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 Euler-Mascheroni constant, p. 31, 1.5.2 Integrals.
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LINKS
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FORMULA
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Equals -(1/4)*sqrt(Pi)*(EulerGamma + 2*log(2)).
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EXAMPLE
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-0.87005772672831550673464879953608743750810733362594...
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MATHEMATICA
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RealDigits[-(1/4)*Sqrt[Pi]*( EulerGamma + 2*Log[2]), 10, 102] // First
RealDigits[NIntegrate[Exp[-x^2]Log[x], {x, 0, \[Infinity]}, WorkingPrecision->120], 10, 120][[1]] (* Harvey P. Dale, Mar 29 2024 *)
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PROG
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(PARI) -(1/4)*sqrt(Pi)*(Euler + 2*log(2)) \\ Michel Marcus, Sep 09 2014
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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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