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A263202 Decimal expansion of the lowest Dirichlet eigenvalue of the Laplacian within the unit-edged regular hexagon. 1

%I

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

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

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

%N Decimal expansion of the lowest Dirichlet eigenvalue of the Laplacian within the unit-edged regular hexagon.

%H Robert Stephen Jones, <a href="/A263202/b263202.txt">Table of n, a(n) for n = 1..1001</a>

%H L. Bauer and E. L. Reiss, <a href="http://www.researchgate.net/publication/202846469_Cutoff_Wavenumbers_and_Modes_of_Hexagonal_Waveguides">Cutoff wavenumbers and modes of hexagonal waveguides</a>, SIAM J. of Appl. Math., 35 (1978), 508-514. (Note: 6-digit results.)

%H L. M. Cureton and J. R. Kuttler, <a href="http://dx.doi.org/10.1006/jsvi.1998.1919">Eigenvalues of the Laplacian on regular polygons and polygons resulting from their dissection</a>, Journal of Sound and Vibration, 220 (1998), 83-98. (Note: Table 2 presents their 8-digit digit results.)

%H Robert S. Jones, <a href="http://arxiv.org/abs/1602.08636">Computing ultra-precise eigenvalues of the Laplacian within polygons</a>, arXiv preprint arXiv:1602.08636, 2016

%e 7.1553391339260551282100176168331392806691995857769779...

%Y Cf. A262701 (L-shape) and A262823 (regular pentagon).

%K nonn,cons

%O 1,1

%A _Robert Stephen Jones_, Oct 12 2015

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Last modified October 23 10:10 EDT 2018. Contains 316525 sequences. (Running on oeis4.)