A247017 Decimal expansion of integral_{0..infinity} exp(-x^2)*log(x) dx.

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

Offset: 0

Author

Jean-François Alcover, Sep 09 2014

Keywords

• nonn
• cons
• easy

Examples

			-0.87005772672831550673464879953608743750810733362594...
		

References

• Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 1.5 Euler-Mascheroni constant, p. 31, 1.5.2 Integrals.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000

Crossrefs

Cf. A020759.

Programs

Mathematica

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 *)

PARI

-(1/4)*sqrt(Pi)*(Euler + 2*log(2)) \\ Michel Marcus, Sep 09 2014

Formula

Equals -(1/4)*sqrt(Pi)*(EulerGamma + 2*log(2)).