Papers › Investigation into the role of the Bessel function order in the Fourier-Bessel series...
Investigation into the role of the Bessel function order in the Fourier-Bessel series and the Hankel Transform
Suketu P Patni, Vikram M Gadre
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 nᵗʰ 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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