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A249185 Decimal expansion of a constant appearing in the Hankel determinant asymptotics.

%I A249185 #15 Feb 16 2025 08:33:24
%S A249185 6,4,5,0,0,2,4,4,8,5,0,9,5,7,7,0,8,4,6,5,8,9,6,1,0,0,7,7,2,1,7,8,7,6,
%T A249185 5,5,3,4,7,6,1,4,4,9,4,0,5,7,3,3,9,7,2,1,5,5,2,1,4,4,5,8,8,5,8,0,2,7,
%U A249185 6,0,7,8,7,4,1,2,4,6,8,4,6,5,7,3,9,7,1,0,5,4,9,7,1,9,7,4,0,9,9,1,4,6
%N A249185 Decimal expansion of a constant appearing in the Hankel determinant asymptotics.
%H A249185 Steven Finch, <a href="/A249185/a249185.pdf">Hankel and Toeplitz Determinants</a>, March 17, 2014. [Cached copy, with permission of the author]
%H A249185 Steven R. Finch, <a href="https://doi.org/10.1017/9781316997741">Mathematical Constants II</a>, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 416.
%H A249185 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/HilbertMatrix.html">Hilbert matrix</a>
%H A249185 Wikipedia, <a href="http://en.wikipedia.org/wiki/Hilbert_matrix">Hilbert matrix</a>
%F A249185 Det(H_n) ~ h*4^(-n^2)*(2*Pi)^n*n^(-1/4), where h = 2^(1/12)*e^(1/4)*A^(-3), A denoting the Glaisher-Kinkelin constant.
%e A249185 0.645002448509577084658961007721787655347614494...
%p A249185 evalf(limit(2^(1/12) * n^(3*n^2/2 + 3*n/2 + 1/4) * exp(1/4-3*n^2/4) / product(k^(3*k), k=1..n), n=infinity),120); # _Vaclav Kotesovec_, Oct 23 2014
%t A249185 h = 2^(1/12)*E^(1/4)*Glaisher^-3; RealDigits[h, 10, 102] // First
%Y A249185 Cf. A005249, A074962.
%K A249185 nonn,cons,easy
%O A249185 0,1
%A A249185 _Jean-François Alcover_, Oct 23 2014