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A276813 Continued fraction for the ratio of the lowest two Dirichlet eigenvalues of the Laplacian within the regular pentagon. 1

%I

%S 2,1,1,8,1,4,2,2,16,3,3,1,3,1,1,2,1,1,3,1,3,3,5,1,13,1,4,1,1,13,4,3,1,

%T 4,1,1,6,5,9,1,13,2,15,1,2,3,3,1,4,9,2,14,1,4,1,7,1,1,11,1,4,5,2,3,2,

%U 1,14,1,1,2,1,1,1,1,20,3,2,1,2,2,7,1,2

%N Continued fraction for the ratio of the lowest two Dirichlet eigenvalues of the Laplacian within the regular pentagon.

%C The eigenvalues of the Laplacian within the regular pentagon with Dirichlet boundary conditions are calculated to at least 1000 digits. The ratio of the second eigenvalue to the first is calculated and expressed as a continued fraction. The ratio has an advantage since it is independent of the pentagon area. All terms in this expansion are correct.

%H Robert Stephen Jones, <a href="/A276813/b276813.txt">Table of n, a(n) for n = 1..978</a>

%e 2.52683872... = 2+1/(1+1/(1+1/(8+1/(1+...)))).

%Y Cf. A262823.

%K nonn,cofr

%O 1,1

%A _Robert Stephen Jones_, Sep 18 2016

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Last modified August 21 10:36 EDT 2018. Contains 313937 sequences. (Running on oeis4.)