Summary
A numerical method is developed which handles the Bessel transform of functions having slow rates of decrease. The method replaces the Bessel transform by a related damped transform for which the sinc quadrature rule provides an efficient and accurate approximation. It is then shown that the value of the original Bessel transform can be obtained from the damped transform by extrapolation with the Thiele algorithm.
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Lund, J. Bessel transforms and rational extrapolation. Numer. Math. 47, 1–14 (1985). https://doi.org/10.1007/BF01389872
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DOI: https://doi.org/10.1007/BF01389872