A243525 Decimal expansion of the variance of the maximum of a size 6 sample from a normal (0,1) distribution.

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

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..99.

Formula

-((225*(Pi*(Pi-4*arccsc(Sqrt(3))) + 2*integral_(x=0..arccsc(sqrt(3)))(arcsin(sqrt(3)*sqrt(1/(8-tan(x)^2)))))^2)/(4*Pi^5))+(5*sqrt(3)*(Pi-3*arccsc(2*sqrt(2/3))))/Pi^2+1

Example

0.415927108983248119181409058601893424...

Mathematica

digits = 100; v[6] = -((225*(Pi*(Pi - 4*ArcCsc[Sqrt[3]]) + 2*NIntegrate[ArcSin[Sqrt[3]*Sqrt[1/(8 - Tan[x]^2)]], {x, 0, ArcCsc[Sqrt[3]]}, WorkingPrecision -> digits+5])^2)/(4*Pi^5)) + (5*Sqrt[3]*(Pi - 3*ArcCsc[2*Sqrt[2/3]]))/Pi^2 + 1; RealDigits[v[6], 10, digits] // First

Crossrefs

Cf. A188340, A243447, A243452, A243454, A243523.

Sequence in context: A139356 A318359 A209297 * A300071 A155060 A153426

Adjacent sequences: A243522 A243523 A243524 * A243526 A243527 A243528

Keyword

nonn,cons

Author

Jean-François Alcover, Jun 06 2014

Status

approved