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

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, 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, 1, 14, 1, 1, 2, 1, 1, 1, 1, 20, 3, 2, 1, 2, 2, 7, 1, 2

Offset: 1

Author

Robert Stephen Jones, Sep 18 2016

Keywords

• nonn
• cofr

Comments

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.

Examples

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

Links

• Robert Stephen Jones, Table of n, a(n) for n = 1..978

Crossrefs

Cf. A262823.