The asymptotic expansion of bessel functions of large order

@article{Olver1954TheAE,
  title={The asymptotic expansion of bessel functions of large order},
  author={Frank W. J. Olver},
  journal={Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences},
  year={1954},
  volume={247},
  pages={328 - 368}
}
  • F. Olver
  • Published 28 December 1954
  • Mathematics
  • Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
New expansions are obtained for the functions Iv{yz), ) and their derivatives in terms of elementary functions, and for the functions J v(vz), Yv{vz), H fvz) and their derivatives in terms of Airy functions, which are uniformly valid with respect to z when | | is large. New series for the zeros and associated values are derived by reversion and used to determine the distribution of the zeros of functions of large order in the z-plane. Particular attention is paid to the complex zeros of 7„(z… 

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  • 1954
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