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

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, 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, 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

Offset

0,1

Links

Table of n, a(n) for n=0..101.

Steven Finch, Hankel and Toeplitz Determinants, March 17, 2014. [Cached copy, with permission of the author]

Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 416.

Eric Weisstein's MathWorld, Hilbert matrix

Wikipedia, Hilbert matrix

Formula

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.

Example

0.645002448509577084658961007721787655347614494...

Maple

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

Mathematica

h = 2^(1/12)*E^(1/4)*Glaisher^-3; RealDigits[h, 10, 102] // First

Crossrefs

Cf. A005249, A074962.

Sequence in context: A019174 A019166 A058158 * A021159 A106332 A247319

Adjacent sequences: A249182 A249183 A249184 * A249186 A249187 A249188

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Oct 23 2014

Status

approved