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Common zeros of two Bessel functions

Authors: T. C. Benton and H. D. Knoble
Journal: Math. Comp. 32 (1978), 533-535
MSC: Primary 33A40; Secondary 65D20
MathSciNet review: 0481160
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Abstract: There is a theorem that two Bessel functions $ {J_\mu }(x)$ and $ {J_\nu }(x)$ can have no common positive zeros if $ \mu $ is an integer and $ \nu = \mu + m$ where m is an integer, but this does not preclude the possibility that for unrestricted real positive $ \mu $ and $ \nu $ not differing by an integer, the two functions $ {J_\mu }(x)$ and $ {J_\nu }(x)$ can have common zeros. An example is found where two such functions have two positive zeros in common.

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

  • [1] R. P. BRENT, "An algorithm with guaranteed convergence for finding a zero of a function," Comput. J., v. 14, 1971, pp. 422-425; in particular see the FORTRAN implementation entitled "ZBRENT" by International Mathematical and Statistical Libraries, Inc., 5th ed., Houston, 1975. MR 0339475 (49:4234)
  • [2] W. GAUTSCHI, "Algorithm 236, Bessel functions of the first kind," Comm. ACM, v. 7, 1964, pp. 479-480.
  • [3] HARVARD COMPUTATION LABORATORY, Tables of Bessel Functions, 1947-1951 Annals, vols. III-XIV, Harvard Univ. Press, Cambridge, Mass.
  • [4] F. W. J. OLVER, "... Evaluation of zeros of Bessel functions...," Proc. Cambridge Philos. Soc., v. 47, 1951, pp. 699-712. MR 0043551 (13:283c)
  • [5] ROYAL SOCIETY, Mathematical Tables 7, Bessel Functions III, edited by F. W. J. Olver, published for the Royal Society by Cambridge Univ. Press, 1960. MR 0119441 (22:10202)
  • [6] G. N. WATSON, Bessel Functions, 4th ed., Cambridge Univ. Press, 1944. MR 0010746 (6:64a)

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Article copyright: © Copyright 1978 American Mathematical Society

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