

A262701


Decimal expansion of lowest Dirichlet eigenvalue of the Laplacian within a certain Lshaped region.


2



9, 6, 3, 9, 7, 2, 3, 8, 4, 4, 0, 2, 1, 9, 4, 1, 0, 5, 2, 7, 1, 1, 4, 5, 9, 2, 6, 2, 3, 6, 4, 8, 2, 3, 1, 5, 6, 2, 6, 7, 2, 8, 9, 5, 2, 5, 8, 2, 1, 9, 0, 6, 4, 5, 6, 1, 0, 9, 5, 7, 9, 7, 0, 0, 5, 6, 4, 0, 3, 5, 6, 4, 7, 8, 6, 3, 3, 7, 0, 3, 9, 0, 7, 2, 2, 8, 7, 3, 1, 6, 5, 0, 0, 8, 7, 9, 6, 7, 8, 8, 8, 3, 1, 1, 5
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OFFSET

1,1


COMMENTS

This is the lowest Dirichlet eigenvalue of the Laplacian within the famous Lshape formed by joining two unitedged squares to adjacent edges of a third. The familiar logo of MathWorks, publisher of MATLAB, is created from the corresponding lowest eigenfunction, with some artistic license. I simply extended the original FoxHenriciMoler 1967 eigenvalue calculation to just over 1000 digits using a method substantially identical to the method described in the Fox et al. paper.


LINKS

Robert Stephen Jones, Table of n, a(n) for n = 1..1001
Paolo Amore, John P. Boyd, Francisco M. Fernandez, Boris RÃ¶sler, High order eigenvalues for the Helmholtz equation in complicated nontensor domains through Richardson Extrapolation of second order finite differences, arXiv:1509.02795 [physics.compph], 2015.
Timo Betcke and Lloyd N. Trefethen, Reviving the method of particular solutions, SIAM Rev., 47 (2004), 469491; Oxford, eprints.maths.ox.ac.uk, pdf.
L. Fox, P. Henrici, and C. Moler, Approximations and bounds for eigenvalues of elliptic operators, SIAM J. Numer. Anal., 4 (1967), 89102; blogs.mathworks.com, eprint, pdf
Robert S. Jones, Computing ultraprecise eigenvalues of the Laplacian within polygons, arXiv preprint arXiv:1602.08636, 2016
MathWorks, The mathworks logo is an eigenfunction of the wave equation
Wikipedia, Dirichlet eigenvalue


EXAMPLE

9.639723844021941052711459262364823156267289525821906456109579700564035647863370...


CROSSREFS

Sequence in context: A259469 A241993 A099817 * A200280 A198363 A253267
Adjacent sequences: A262698 A262699 A262700 * A262702 A262703 A262704


KEYWORD

nonn,cons


AUTHOR

Robert Stephen Jones, Sep 27 2015


STATUS

approved



