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Decimal expansion of the variance of the maximum of a size 5 sample from a normal (0,1) distribution.
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%I #5 Jun 05 2014 11:35:00

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

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

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

%N Decimal expansion of the variance of the maximum of a size 5 sample from a normal (0,1) distribution.

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

%F 1 - 25/Pi + 150*arccsc(sqrt(3))/Pi^2 + 5*sqrt(3)*arcsec(2*sqrt(2/3))/Pi^2 - 225*arccsc(sqrt(3))^2/Pi^3.

%e 0.44753406902066198876568465773...

%t RealDigits[1 - 25/Pi + 150*ArcCsc[Sqrt[3]]/Pi^2 + 5*Sqrt[3]*ArcSec[2*Sqrt[2/3]]/Pi^2 - 225*ArcCsc[Sqrt[3]]^2/Pi^3, 10, 101] // First

%Y Cf. A087197, A188340, A243446, A243447, A243448, A243452, A243453.

%K nonn,cons,easy

%O 0,1

%A _Jean-François Alcover_, Jun 05 2014