OFFSET
1,1
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.15 Glaisher-Kinkelin Constant, p. 136.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..5000
Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 20.
Eric Weisstein's MathWorld, Barnes G-Function
Eric Weisstein's MathWorld, Glaisher-Kinkelin Constant
FORMULA
D(x) = lim_{n->infinity} ( Prod_{k=1..2n+1} (1+x/k)^((-1)^(k+1)*k) ).
D(x) = (e^(x/2-1/4)*A^3*G((x+1)/2)^2*Gamma(x/2)^(x-2)*Gamma((x+1)/2)^(1-x)*(Gamma((x+1)/2)/Gamma(x/2))^x)/(2^(1/12)*G(x/2)^2), where A is the Glaisher-Kinkelin constant and G is the Barnes G-function.
D(1) = A^6/(2^(1/6)*sqrt(Pi)).
EXAMPLE
2.23588559550896986428396479931189064484515912285952474779344797826...
MATHEMATICA
RealDigits[Glaisher^6/(2^(1/6)*Sqrt[Pi]), 10, 104] // First
PROG
(PARI) default(realprecision, 100); A=exp(1/12-zeta'(-1)); A^6/(2^(1/6)* sqrt(Pi)) \\ G. C. Greubel, Aug 24 2018
CROSSREFS
KEYWORD
AUTHOR
Jean-François Alcover, Aug 08 2014
STATUS
approved