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

Abstract

I reconsider the approximation of Bessel functions with finite sums of trigonometric functions, in the light of recent evaluations of Neumann-Bessel series with trigonometric coefficients. A proper choice of the angle allows for an efficient choice of the trigonometric sum. Based on these series, I also obtain straightforward non-standard evaluations of new parametric sums with powers of cosine and sine functions.

9 pages

References in corpus (2)

• Some Neumann-Bessel series and the Laplacian on polygons
• Exact evaluations and reciprocity theorems for finite trigonometric sums

Cited by in corpus (1)

• The Fourier-Legendre series of Bessel functions of the first kind and the summed series involving ${}_2{F}_3$ hypergeometric functions that arise from them