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  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 48, Issue 3
  • July 1952, pp. 414-427

Some new asymptotic expansions for Bessel functions of large orders

  • F. W. J. Olver (a1)
  • DOI:
  • Published online: 24 October 2008

During the course of recent work (6) on the zeros of the Bessel functions Jn(x) and Yn(x), it became evident that the theory of the asymptotic expansion of Bessel functions whose arguments and orders are of comparable magnitudes was incomplete. The existing expansions for large orders are those of Debye and Meissel, detailed derivations of both of which are given by Watson ((8), pp. 237–48).

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(3)I. Imai Asymptotic solutions of ordinary differential equations of the second order. Phys. Rev. (2), 80 (1950), 1112.

(4)R. E. Langer On the asymptotic solutions of ordinary differential equations with application to Bessel functions of large order. Trans. Amer. math. Soc. 33 (1931), 2364.

(5)J. W. Nicholson The asymptotic expansion of Bessel functions. Phil. Mag. (6), 19 (1910), 228–49.

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