A059444 Decimal expansion of square root of (Pi * e / 2).

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

Offset: 1

Author

Robert G. Wilson v, Feb 01 2001

Keywords

• nonn
• cons

Comments

Appears as constant factor in Proposition 1.12, p. 5, of Feige et al. (2007). - Jonathan Vos Post, Jun 18 2007

Examples

			2.066365677...
		

References

• C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Oxford University Press, Oxford and NY, 2001, page 68.

Links

• Harry J. Smith, Table of n, a(n) for n = 1..20000
• C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Zentralblatt review
• Uri Feige, Guy Kindler, Ryan O Donnell, Understanding Parallel Repetition Requires Understanding Foams, Electronic Colloquium on Computational Complexity, Report TR07-043 (ISSN 1433-8092, 14th Year, 43rd Report), 7 May 2007.
• OEIS Wiki, A remarkable formula of Ramanujan

Crossrefs

Cf. A059445, A060196, A108088.

Programs

Mathematica

RealDigits[N[Sqrt[ \[Pi]*\[ExponentialE]/2], 100]][[1]]
RealDigits[Sqrt[(Pi*E)/2],10,120][[1]] (* Harvey P. Dale, Nov 27 2024 *)

PARI

{ default(realprecision, 20080); x=sqrt(Pi*exp(1)/2); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b059444.txt", n, " ", d)); } \\ Harry J. Smith, Jun 27 2009

Formula

Sqrt(Pi*e/2) = A + B with A = 1 + 1/(1*3) + 1/(1*3*5) + 1/(1*3*5*7) + 1/(1*3*5*7*9) + ... = 1.410686134... (see A060196) and B = 1/(1 + 1/(1 + 2/(1 + 3/(1 + 4/(1 + 5/(1 + ...)))))) = 0.65567954241... (see A108088) - (S. Ramanujan)

Equals (sqrt(2)*exp(1/4)*(sum(n>=0, n!/(2*n)! ) - 1))/erf(1/2). - Jean-François Alcover, Mar 22 2013

Extensions

Edited by Daniel Forgues, Apr 14 2011