Some Neumann-Bessel series and the Laplacian on polygons

Abstract

Several sums of Neumann series with Bessel and trigonometric functions are evaluated, as finite sums of trigonometric functions. They arise from a generalization of the Neumann expansion of the eigenstates of the Laplacian in regular polygons.

arXiv comment7 pages, 8 figures

References in corpus (1)

• The fundamental Laplacian eigenvalue of the regular polygon with Dirichlet boundary conditions

Cited by in corpus (1)

• A note on trigonometric approximations of Bessel functions of the first kind and trigonometric power sums