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

Author

Jean-François Alcover, Jun 06 2014

Keywords

• nonn
• cons

Examples

			0.415927108983248119181409058601893424...
		

References

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

Crossrefs

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

Programs

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

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