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Decimal expansion of C = 2^(1/3)*e^(1/4)/A^3, a constant associated with the Gaudin-Mehta probability distribution and the Glaisher-Kinkelin constant A.
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%I #9 Jul 25 2024 03:13:18

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

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

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

%N Decimal expansion of C = 2^(1/3)*e^(1/4)/A^3, a constant associated with the Gaudin-Mehta probability distribution and the Glaisher-Kinkelin constant A.

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.15 Glaisher-Kinkelin constant, p. 140.

%H Dan Bump, <a href="http://empslocal.ex.ac.uk/people/staff/mrwatkin//zeta/bump-gue.htm">The Gaussian Unitary Ensemble Hypothesis</a>.

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

%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/RandomMatrix.html">Random Matrix</a>.

%F C = 2^(1/3)*exp(3*zeta'(-1)) = 2^(1/4)*exp(2*B), where B is A243999.

%e 0.7670415009617653094127391775868208813020937515...

%t RealDigits[2^(1/3)*E^(1/4)/Glaisher^3, 10, 108] // First

%o (PARI) 2^(1/3)*exp(3*zeta'(-1)) \\ _Amiram Eldar_, Jul 25 2024

%Y Cf. A074962(A), A084448(zeta'(-1)), A243999(B).

%K nonn,cons,easy

%O 0,1

%A _Jean-François Alcover_, Sep 12 2014