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 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.

Keywords

• Bessel functions
• Neumann series
• Trigonometric approximations
• Trigonometric power sum

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