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 A243964 Decimal expansion of the variance of the maximum of a size 8 sample from a normal (0,1) distribution. 0
 3, 7, 2, 8, 9, 7, 1, 4, 3, 2, 8, 6, 7, 2, 8, 9, 9, 4, 2, 2, 0, 2, 1, 1, 2, 2, 8, 7, 6, 2, 1, 1, 4, 6, 0, 2, 1, 7, 6, 3, 5, 9, 2, 9, 2, 0, 0, 0, 4, 6, 7, 3, 7, 5, 7, 9, 5, 7, 8, 4, 9, 1, 7, 6, 7, 2, 4, 8, 9, 4, 6, 2, 1, 5, 3, 8, 5, 0, 7, 7, 7, 9, 6, 3, 0, 6, 7, 5, 7, 3, 9, 8, 0, 1, 0, 4, 5, 7, 6, 2, 9 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS According to Steven Finch, no exact expression of this moment is known. REFERENCES Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.16 Extreme value constants, p. 365. LINKS FORMULA integral_(-infinity..infinity) 8*x^2*F(x)^7*f(x) dx - mu(8)^2, where f(x) is the normal (0,1) density and F(x) its cumulative distribution, mu(8) being the moment A243961. EXAMPLE 0.3728971432867289942202112287621146... MATHEMATICA digits = 101; m0 = 5; dm = 5; f[x_] := 1/ Sqrt[2*Pi]*Exp[-x^2/2]; F[x_] := 1/2*Erf[x/Sqrt[2]] + 1/2; Clear[mu8]; mu8[m_] := mu8[m] = 8*NIntegrate[x*F[x]^7*f[x], {x, -m , m}, WorkingPrecision -> digits+5, MaxRecursion -> 20]; mu8[m0]; mu8[m = m0+dm]; While[RealDigits[mu8[m]] != RealDigits[mu8[m-dm]], Print["m1 = ", m]; m = m+dm]; m8 = mu8[m]; Clear[v, m]; v[m_] := v[m] = 8*NIntegrate[x^2*F[x]^7*f[x], {x, -m , m}, WorkingPrecision -> digits+5, MaxRecursion -> 20]; v[m0]; v[m = m0+dm]; While[RealDigits[v[m]] != RealDigits[v[m-dm]], Print["m2 = ", m]; m = m+dm]; v8 = v[m]-m8^2; RealDigits[v8, 10, digits] // First CROSSREFS Cf. A188340 v(2), A243447 v(3), A243452 v(4), A243454 v(5), A243525 v(6), A243526 v(7), A243961 mu(8). Sequence in context: A199401 A261573 A159759 * A197837 A222070 A163917 Adjacent sequences:  A243961 A243962 A243963 * A243965 A243966 A243967 KEYWORD nonn,cons AUTHOR Jean-François Alcover, Jun 16 2014 STATUS approved

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