A261873 Decimal expansion of H(1/2,1), a constant appearing in the asymptotic variance of the largest component of random mappings on n symbols, expressed as H(1/2,1)*n^2.

0, 3, 7, 0, 0, 7, 2, 1, 6, 5, 8, 2, 2, 9, 0, 3, 0, 3, 2, 0, 9, 9, 2, 3, 7, 8, 9, 4, 4, 8, 9, 1, 9, 3, 3, 0, 0, 7, 0, 0, 7, 3, 9, 8, 0, 6, 2, 1, 3, 2, 8, 4, 7, 3, 6, 3, 8, 5, 0, 5, 7, 3, 0, 5, 9, 7, 0, 9, 3, 6, 6, 0, 0, 7, 7, 3, 2, 8, 3, 1, 2, 8, 0, 6, 7, 1, 0, 1, 0, 7, 7, 6, 7, 7, 9, 4, 9, 3, 7, 6, 4, 9, 6, 1, 3, 2

Offset: 0

Author

Jean-François Alcover, Sep 04 2015

Keywords

• nonn
• cons
• easy

Examples

			0.037007216582290303209923789448919330070073980621328473638505730597...
		

References

• Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.4.2 Random Mapping Statistics, p. 289.

Crossrefs

Cf. A143297.

Programs

Mathematica

digits = 105; h1 = (8/3)*NIntegrate[(1 - Exp[ExpIntegralEi[-x]/2])*x, {x, 0, Infinity}, WorkingPrecision -> digits + 10]; h2 = 4*NIntegrate[1 - Exp[ExpIntegralEi[-x]/2], {x, 0, Infinity}, WorkingPrecision -> digits + 10]^2 ; Join[{0}, RealDigits[h1 - h2, 10, digits] // First]

Formula

H(1/2,1) = (8/3) Integral_{0..infinity} (1-exp(Ei(-x)/2)) x dx - A143297^2, where A143297 is G(1/2,1), using Finch's notation.