A243526 Decimal expansion of the variance of the maximum of a size 7 sample from a normal (0,1) distribution.

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

Offset

0,1

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.16 Extreme value constants, p. 365.

Links

Table of n, a(n) for n=0..98.

Formula

-((441*(Pi*(Pi - 5*arccsc(sqrt(3))) + 5*integral_(x=0..arccsc(sqrt(3)) )(arcsin(sqrt(3)*sqrt(1/(8 - tan(x)^2))), {x, 0, arccsc(sqrt(3))} ))^2)/(4*Pi^5)) + (35*sqrt(3)*(Pi*(Pi - 4*arccsc(2*sqrt(2/3))) + 2*integral_(x=0..arccsc(2*sqrt(2/3)))(arcsin(sqrt(6)*sqrt(1/(15 - tan(x)^2))), {x, 0, arccsc(2*sqrt(2/3))} )))/(4*Pi^3) + 1

Example

0.39191777612675045281968496580009199872...

Mathematica

digits = 99; v[7] = -((441*(Pi*(Pi - 5*ArcCsc[Sqrt[3]]) + 5*NIntegrate[ArcSin[Sqrt[3]*Sqrt[1/(8 - Tan[x]^2)]], {x, 0, ArcCsc[Sqrt[3]]},
WorkingPrecision -> digits + 5])^2)/(4*Pi^5)) + (35*Sqrt[3]*(Pi*(Pi - 4*ArcCsc[2*Sqrt[2/3]]) + 2*NIntegrate[ArcSin[Sqrt[6]*Sqrt[1/(15 - Tan[x]^2)]], {x, 0, ArcCsc[2*Sqrt[2/3]]}, WorkingPrecision -> digits + 5]))/(4*Pi^3) + 1; RealDigits[v[7], 10, digits] // First

Crossrefs

Cf. A188340, A243447, A243452, A243454, A243525, A243524.

Sequence in context: A333346 A165141 A019817 * A329214 A080322 A126179

Adjacent sequences: A243523 A243524 A243525 * A243527 A243528 A243529

Keyword

nonn,cons

Author

Jean-François Alcover, Jun 06 2014

Status

approved