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On Bessel functions and rate of convergence of zeros of Lommel polynomials

Authors: P. Feinsilver and R. Schott
Journal: Math. Comp. 59 (1992), 153-156
MSC: Primary 33C10; Secondary 33C45
MathSciNet review: 1134728
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Abstract: In this note, we solve an open problem of Flajolet and Schott concerning the rate of convergence of the zeros of Lommel polynomials to the zeros of a Bessel function (considered as a function of the order). The average case analysis of dynamic data structures was the initial motivation for this investigation. The Maple program, whose results are reported at the end, illustrates that our result is quite good.

References [Enhancements On Off] (What's this?)

  • [1] J. Coulomb, Sur les zéros des fonctions de Bessel considérées comme fonction de l'ordre, Bull. Sci. Math. 60 (1936), 297-302.
  • [2] Philippe Flajolet and René Schott, Nonoverlapping partitions, continued fractions, Bessel functions and a divergent series, European J. Combin. 11 (1990), no. 5, 421–432. MR 1075531, 10.1016/S0195-6698(13)80025-X
  • [3] G. N. Watson, A treatise on the theory of Bessel functions, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1995. Reprint of the second (1944) edition. MR 1349110

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Article copyright: © Copyright 1992 American Mathematical Society