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MR1723000 (2000k:33005) 33C10 (33F05 41A60 65D20)
Fabijonas, Bruce R.; Olver, F. W. J. On the reversion of an asymptotic expansion and the zeros of the Airy functions. SIAM Rev. 41 (1999), no. 4, 762–773 (electronic).
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