A263202 Decimal expansion of the lowest Dirichlet eigenvalue of the Laplacian within the unit-edged regular hexagon.
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, 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, 3, 3, 1, 2, 2, 5, 0, 9, 2, 5, 3, 3, 7, 5, 4, 8, 7, 5
Offset: 1
Examples
7.1553391339260551282100176168331392806691995857769779...
Links
- Robert Stephen Jones, Table of n, a(n) for n = 1..1001
- L. Bauer and E. L. Reiss, Cutoff wavenumbers and modes of hexagonal waveguides, SIAM J. of Appl. Math., 35 (1978), 508-514. (Note: 6-digit results.)
- L. M. Cureton and J. R. Kuttler, Eigenvalues of the Laplacian on regular polygons and polygons resulting from their dissection, Journal of Sound and Vibration, 220 (1998), 83-98. (Note: Table 2 presents their 8-digit digit results.)
- Robert S. Jones, Computing ultra-precise eigenvalues of the Laplacian within polygons, arXiv preprint arXiv:1602.08636, 2016