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. A simple accurate approximation of J0(x) is found on the interval [0, 2].
Some Neumann-Bessel series and the Laplacian on polygons / L.G. Molinari. - In: JOURNAL OF MATHEMATICAL PHYSICS. - ISSN 0022-2488. - 62:5(2021), pp. 053502.1-053502.7.
Some Neumann-Bessel series and the Laplacian on polygons
L.G. Molinari
2021
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. A simple accurate approximation of J0(x) is found on the interval [0, 2].
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