A241140 Decimal expansion of an infinite product involving the ratio of n! to its Stirling approximation.

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

Offset: 1

Author

Jean-François Alcover, Aug 08 2014

Keywords

• nonn
• cons
• easy

Comments

The same product where the ratio is replaced by sqrt(2*Pi) evaluates as (2*Pi)^(1/4) = 1.58323...

Examples

			1.057328141001876924952657094184286643131791252628433822095146...
		

References

• Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.15 Glaisher-Kinkelin Constant, p. 135.

Links

• Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 20.
• Eric Weisstein's MathWorld, Glaisher-Kinkelin Constant

Crossrefs

Cf. A019727, A074962.

Programs

Mathematica

RealDigits[Glaisher^3/(2^(7/12)*Pi^(1/4)), 10, 101] // First

Formula

Product_{n>=1} (n! / ((sqrt(2*Pi*n)*n^n)/e^n))^((-1)^(n-1)) = A^3/(2^(7/12)*Pi^(1/4)), where A is the Glaisher-Kinkelin constant.