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Monotonicity in terms of order of the zeros of the derivatives of Bessel functions

Author: Lee Lorch
Journal: Proc. Amer. Math. Soc. 108 (1990), 387-389
MSC: Primary 33A40
MathSciNet review: 993757
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Abstract: An elementary Sturm technique is shown to provide an alternative and simpler proof of the result that the known monotonicity of the zeros of fixed rank of the Bessel function of the first kind implies monotonicity for the zeros of its derivative for orders between -1 and 0. The reasoning applies to other Bessel functions.

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  • [1] M. Bôcher, On certain methods of Sturm and their applications to the roots of Bessel's functions, Bull. Amer. Math. Soc. 3 (1897), 205-213. MR 1557505
  • [2] M. E. H. Ismail and M. E. Muldoon, On the variation with respect to a parameter of zeros of Bessel and $ q$-Bessel functions, J. Math. Anal, and Appl. 135 (1988), 187-207. MR 960813 (89i:33011)
  • [3] L. Lorch, Elementary comparison techniques for certain classes of Sturm-Liouville equations, in Proc. Uppsala 1977 Inter. Conf. Diff. Equations, Symposia Univ. Upsaliensis Annum Quingentesimum Celebrantis 7, Acta Univ. Upsaliensis, Uppsala 1977, 125-133. MR 0492536 (58:11644)
  • [4] L. Lorch and P. Szego, On the zeros of derivatives of Bessel functions, SIAM J. Math. Anal. 19 (1988), 1450-1454. MR 965265 (90c:33017)
  • [5] F. W. J. Olver, Asymptotics and special functions, Academic Press, New York and London, 1974. MR 0435697 (55:8655)
  • [6] G. N. Watson, A treatise on the theory of Bessel functions, 2nd ed., The University Press, Cambridge, 1952. MR 1349110 (96i:33010)

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