A243524 Decimal expansion of the expectation of the maximum of a size 7 sample from a normal (0,1) distribution.

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

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

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

Example

1.3521783756069043992289221668285773452932858435...

Mathematica

digits = 100; mu[7] = (21*(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* Pi^(5/2)); RealDigits[mu[7], 10, digits] // First

Crossrefs

Cf. A087197, A243446, A243448, A243453, A243523.

Sequence in context: A329633 A126353 A094791 * A349988 A272300 A115406

Adjacent sequences: A243521 A243522 A243523 * A243525 A243526 A243527

Keyword

nonn,cons

Author

Jean-François Alcover, Jun 06 2014

Status

approved