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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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On Bessel functions and rate of convergence of zeros of Lommel polynomials
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by P. Feinsilver and R. Schott PDF
Math. Comp. 59 (1992), 153-156 Request permission

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
    J. Coulomb, Sur les zéros des fonctions de Bessel considérées comme fonction de l’ordre, Bull. Sci. Math. 60 (1936), 297-302.
  • 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, DOI 10.1016/S0195-6698(13)80025-X
  • 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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Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Math. Comp. 59 (1992), 153-156
  • MSC: Primary 33C10; Secondary 33C45
  • DOI: https://doi.org/10.1090/S0025-5718-1992-1134728-9
  • MathSciNet review: 1134728