On Dirichlet eigenvalues of regular polygons

David Berghaus, Bogdan Georgiev, Hartmut Monien +1

We prove that the first Dirichlet eigenvalue of a regular $N$-gon of area $\pi$ has an asymptotic expansion of the form ${\lambda }_1(1+{\sum }_{n\ge 3}{C}_n({\lambda }_1)N^{-n})$ as $N\to \infty$, where $λ_…