A249415 Decimal expansion of p_0, a constant associated with the Khintchine inequality in case of random variables with Rademacher distribution.

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

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

Steven R. Finch, Moments of sums, April 23, 2004 [Cached copy, with permission of the author]

Wikipedia, Khintchine inequality

Wikipedia, Rademacher distribution

Formula

p_0 is the unique solution of the equation Gamma((p + 1)/2) = sqrt(Pi)/2.

Example

1.8474163360763421293976936897345912119153478325037...

Maple

Digits := 120; `assuming`([fsolve(GAMMA((p+1)/2) = sqrt(Pi)/2)], [p > 0]) # Vaclav Kotesovec, Oct 28 2014

Mathematica

p0 = p /. FindRoot[Gamma[(p + 1)/2] == Sqrt[Pi]/2, {p, 1}, WorkingPrecision -> 104]; RealDigits[p0] // First

Crossrefs

Sequence in context: A176453 A257775 A242023 * A021122 A110233 A179260

Adjacent sequences: A249412 A249413 A249414 * A249416 A249417 A249418

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Oct 28 2014

Status

approved