A229495 Stirling's approximation constant e / sqrt(2*Pi).

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

Offset: 1

Author

John W. Nicholson, Sep 24 2013

Keywords

• nonn
• cons

Examples

			1.0844375514192275466115773134229479858...
		

References

• Ovidiu Furdui, Limits, Series, and Fractional Part Integrals: Problems in Mathematical Analysis, New York: Springer, 2013. See Problem 1.5, pages 2 and 27-28.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• Rafael Jakimczuk, Two Topics in Number Theory: Products Related with the e Number and Sum of Subscripts in Prime Numbers, ResearchGate, May 2025. See p. 2, the constant exp(C) in eq. (2.1).
• Wikipedia, Stirling's approximation.

Crossrefs

Cf. A001113 (e), A019727 (sqrt(2*Pi)), A001142, A110544.

Programs

Magma

SetDefaultRealField(RealField(100)); R:= RealField(); Exp(1)/Sqrt(2*Pi(R)); // G. C. Greubel, Oct 06 2018

Maple

evalf(exp(1)/sqrt(2*Pi),120); # Muniru A Asiru, Oct 07 2018

Mathematica

RealDigits[E/Sqrt[2Pi],10,120][[1]] (* Harvey P. Dale, Jan 21 2017 *)

PARI

exp(1)/sqrt(2*Pi) \\ Ralf Stephan, Sep 26 2013

Formula

Equals exp(1)/sqrt(2*Pi).

Equals lim_{n->oo} (A001142(n)^(1/n)*sqrt(n)/(exp(n/2))) (Furdui, 2013). - Amiram Eldar, Mar 26 2022

Equals Product_{n>=1} (1 + 1/n)^(n+1/2)/e. - Amiram Eldar, Jul 08 2023

Equals exp(A110544). - Amiram Eldar, May 30 2025

Extensions

More terms from Ralf Stephan, Sep 26 2013

Corrected and extended by Harvey P. Dale, Jan 21 2017