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A262701 Decimal expansion of lowest Dirichlet eigenvalue of the Laplacian within a certain L-shaped 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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This is the lowest Dirichlet eigenvalue of the Laplacian within the famous L-shape formed by joining two unit-edged 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 Fox-Henrici-Moler 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 Rösler, High order eigenvalues for the Helmholtz equation in complicated non-tensor domains through Richardson Extrapolation of second order finite differences, arXiv:1509.02795 [physics.comp-ph], 2015.

Timo Betcke and Lloyd N. Trefethen, Reviving the method of particular solutions, SIAM Rev., 47 (2004), 469-491; 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), 89-102; blogs.mathworks.com, eprint, pdf

Robert S. Jones, Computing ultra-precise 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

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Last modified August 20 06:32 EDT 2017. Contains 290824 sequences.