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MR1349103 (97a:65114) 65T20 (65R10)
Zhileĭkin, Ya. M.; Kukarkin, A. B. On an algorithm for the fast Fourier-Bessel transform. (Russian) Zh. Vychisl. Mat. i Mat. Fiz. 35 (1995), no. 7, 1128--1133; translation in Comput. Math. Math. Phys. 35 (1995), no. 7, 901–905
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