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A fast analysis-based discrete Hankel transform using asymptotic expansions
A fast and numerically stable algorithm is described for computing the
discrete Hankel transform of order as well as evaluating Schl\"{o}milch and
Fourier--Bessel expansions in
operations. The algorithm is based on an asymptotic expansion for Bessel
functions of large arguments, the fast Fourier transform, and the Neumann
addition formula. All the algorithmic parameters are selected from error bounds
to achieve a near-optimal computational cost for any accuracy goal. Numerical
results demonstrate the efficiency of the resulting algorithm.Comment: 22 page
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