A093814 Decimal expansion of sqrt(2*Pi/e).

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

Offset: 1

Author

Benoit Cloitre, May 20 2004

Keywords

• cons
• nonn

Comments

Arises in an asymptotic formula for f(x) = Sum_{k>0} (x/k)^k as x->oo: f(x) is asymptotic to sqrt(2*Pi/e)*sqrt(x)*e^(x/e).

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Equals A019727*A092605. - Michel Marcus, Oct 02 2018

Programs

Magma

SetDefaultRealField(RealField(100)); R:= RealField(); Sqrt(2*Pi(R)/Exp(1)); // G. C. Greubel, Oct 01 2018

Mathematica

RealDigits[Sqrt[2*Pi/E],10,120][[1]] (* Harvey P. Dale, Mar 05 2015 *)

PARI

default(realprecision, 100); sqrt(2*Pi/exp(1)) \\ G. C. Greubel, Oct 01 2018

Formula

sqrt(2*Pi/e) = 1.52034690106628080561194...