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Lower bounds for the zeros of Bessel functions


Author: Roger C. McCann
Journal: Proc. Amer. Math. Soc. 64 (1977), 101-103
MSC: Primary 33A40
DOI: https://doi.org/10.1090/S0002-9939-1977-0442316-6
MathSciNet review: 0442316
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ {j_{p,n}}$ denote the nth positive zero of $ {J_p},p \geqslant 0$. Then

$\displaystyle {j_{p,n}} \geqslant {( {j_{0,n}^2 + {p^2}} )^{1/2}}.$


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

  • [1] T.H. Boyer, Concerning the zeros of some functions related to Bessel functions, J. Mathematical Phys. 10 (1969), 1729-1744. MR 41 #2074. MR 0257423 (41:2074)
  • [2] H.W. Hethcote, Error bounds for asymptotic approximations of zeros of transcendental functions, SIAM J. Math Anal. 1 (1970), 147-152. MR 42 #744. MR 0265835 (42:744)
  • [3] -, Bounds for zeros of some special functions, Proc. Amer. Math. Soc. 25 (1970), 72-74. MR 41 #569. MR 0255909 (41:569)
  • [4] M. Kline, Some Bessel equations and their application to guide and cavity theory, J. Mathematical Phys. 27 (1948), 37-48. MR 9, 431. MR 0023961 (9:431b)
  • [5] S.G. Mikhlin, Variational methods in mathematical physics, GITTL, Moscow, 1957; English transl., Macmillan, New York, 1964. MR 22 #1981; 30 #2712. MR 0172493 (30:2712)
  • [6] F.W.J. Olver, The asymptotic expansion of Bessel functions of large order, Philos. Trans. Roy. Soc. London Ser. A247 (1954), 328-368. MR 16, 696. MR 0067250 (16:696a)
  • [7] -(Editor), Bessel functions. Part III, Roy. Soc. Math. Tables, Vol. 7, Cambridge Univ. Press, Cambridge, 1960.
  • [8] F. Tricomi, Sulle funzioni di Bessel di ordine e argomento pressochèuguali, Atti. Accad. Sci. Torino Cl. Sci. Fis. Mat. Nat. 83 (1949), 3-20. MR 11, 594. MR 0034478 (11:594a)
  • [9] G.N. Watson, A treatise on the theory of Bessel functions, Cambridge Univ. Press, Cambridge, 1958. MR 1349110 (96i:33010)

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DOI: https://doi.org/10.1090/S0002-9939-1977-0442316-6
Article copyright: © Copyright 1977 American Mathematical Society

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