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Decimal expansion of (Glaisher^12/(2^(4/3) * Pi * e^EulerGamma))^(Pi^2/8).
1

%I #23 Feb 16 2025 08:33:00

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

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

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

%N Decimal expansion of (Glaisher^12/(2^(4/3) * Pi * e^EulerGamma))^(Pi^2/8).

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.15 Glaisher-Kinkelin constant, p. 135.

%H J. W. Glaisher, <a href="https://gdz.sub.uni-goettingen.de/id/PPN599484047_0024">On the constant which occurs in the formula for 1^1*2^2*3^3*...n^n</a>, Messenger of Mathematics, Vol. 24 (1894-95), pp. 1-16.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Glaisher-KinkelinConstant.html">Glaisher-Kinkelin Constant</a>.

%F Equals Product_{k>=1} (2*k-1)^(1/(2*k-1)^2). - _Amiram Eldar_, Jun 25 2021

%e 1.5190966334421985314...

%t RealDigits[(Glaisher^12/(2^(4/3)Pi E^EulerGamma))^(Pi^2/8),10,100][[1]] (* _Vaclav Kotesovec_, Aug 15 2015 after _Eric W. Weisstein_ *)

%Y Cf. A000796, A001113, A001620, A074962.

%K nonn,cons,changed

%O 1,2

%A _Eric W. Weisstein_, Jan 25 2006

%E Offset corrected by _Amiram Eldar_, Jun 25 2021