login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A249185 Decimal expansion of a constant appearing in the Hankel determinant asymptotics. 1

%I

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

%H Steven Finch, <a href="/A249185/a249185.pdf">Hankel and Toeplitz Determinants</a>, March 17, 2014. [Cached copy, with permission of the author]

%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/HilbertMatrix.html">Hilbert matrix</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Hilbert_matrix">Hilbert matrix</a>

%F 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 0.645002448509577084658961007721787655347614494...

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

%Y Cf. A005249, A074962.

%K nonn,cons,easy

%O 0,1

%A _Jean-Fran├žois Alcover_, Oct 23 2014

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 18 00:56 EDT 2019. Contains 326059 sequences. (Running on oeis4.)