Investigation into the role of the Bessel function order in the Fourier-Bessel series and the Hankel Transform

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• github.com/suketu-patni/fourier_bessel_plots
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Abstract

This work focuses on estimating the number of terms of a Fourier-Bessel series of order p' required to get within a certain error of a Bessel function of a fixed order p where p p'. Our approach consists of two steps: one, constructing an invariant over n of the n^th order Hankel transform; and two, observing the effect of expanding a suitably scaled Bessel function of a fixed order p in its Fourier-Bessel series of order p'. We demonstrate a new error metric to simplify the error computations. Further, we generate an empirical model using numerical simulations and examine its capabilities in predicting the number of terms required.

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