OFFSET
1,3
COMMENTS
The same product where the ratio is replaced by sqrt(2*Pi) evaluates as (2*Pi)^(1/4) = 1.58323...
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
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.
EXAMPLE
1.057328141001876924952657094184286643131791252628433822095146...
MATHEMATICA
RealDigits[Glaisher^3/(2^(7/12)*Pi^(1/4)), 10, 101] // First
CROSSREFS
KEYWORD
AUTHOR
Jean-François Alcover, Aug 08 2014
STATUS
approved