A243523 Decimal expansion of the expectation of the maximum of a size 6 sample from a normal (0,1) distribution.

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

Offset

1,2

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=1..100.

Formula

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

Example

1.26720636061147129764934888186399444269365...

Mathematica

digits=100; mu[6] = (15*(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* Pi^(5/2)) ; RealDigits[mu[6], 10, digits] // First

Crossrefs

Cf. A087197, A243446, A243448, A243453.

Sequence in context: A212223 A158915 A257478 * A011044 A131212 A020771

Adjacent sequences: A243520 A243521 A243522 * A243524 A243525 A243526

Keyword

nonn,cons

Author

Jean-François Alcover, Jun 06 2014

Status

approved