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URL: https://oeis.org/A243961

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A243961
Decimal expansion of the expectation of the maximum of a size 8 sample from a normal (0,1) distribution.
1
1, 4, 2, 3, 6, 0, 0, 3, 0, 6, 0, 4, 5, 2, 7, 7, 7, 5, 3, 0, 7, 8, 3, 2, 4, 6, 4, 9, 3, 0, 6, 2, 5, 7, 2, 5, 3, 0, 8, 6, 7, 2, 5, 2, 7, 0, 6, 9, 4, 8, 3, 1, 4, 3, 2, 2, 2, 5, 9, 1, 7, 5, 5, 4, 7, 8, 3, 5, 5, 5, 1, 2, 6, 8, 5, 2, 8, 1, 4, 2, 1, 6, 4, 2, 8, 9, 8, 8, 6, 5, 9, 7, 6, 9, 2, 7, 5, 5, 3, 7
OFFSET
1,2
COMMENTS
According to Steven Finch, no exact expression of this moment mu(8) is known, unlike the moments mu(n) for n<8.
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.16 Extreme value constants, p. 365.
FORMULA
integral_(-infinity..infinity) 8*x*F(x)^7*f(x) dx, where f(x) is the normal (0,1) density and F(x) its cumulative distribution.
EXAMPLE
1.423600306045277753078324649306257253...
MATHEMATICA
digits = 100; 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["m = ", m]; m = m + dm]; RealDigits[mu8[m], 10, digits] // First
CROSSREFS
Cf. A087197 mu(2), A243446 mu(3), A243448 mu(4), A243453 mu(5), A243523 mu(6), A243524 mu(7).
Sequence in context: A123403 A276957 A275847 * A098317 A371325 A095185
KEYWORD
nonn,cons
AUTHOR
STATUS
approved