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A243526
Decimal expansion of the variance of the maximum of a size 7 sample from a normal (0,1) distribution.
1
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.
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
KEYWORD
nonn,cons
AUTHOR
STATUS
approved