An algorithm for the rapid numerical evaluation of Bessel functions of real orders and arguments

@article{Bremer2019AnAF,
  title={An algorithm for the rapid numerical evaluation of Bessel functions of real orders and arguments},
  author={James Bremer},
  journal={Advances in Computational Mathematics},
  year={2019},
  volume={45},
  pages={173-211}
}
  • J. Bremer
  • Published 22 May 2017
  • Mathematics
  • Advances in Computational Mathematics
We describe a method for the rapid numerical evaluation of the Bessel functions of the first and second kinds of nonnegative real orders and positive arguments. Our algorithm makes use of the well-known observation that although the Bessel functions themselves are expensive to represent via piecewise polynomial expansions, the logarithms of certain solutions of Bessel’s equation are not. We exploit this observation by numerically precomputing the logarithms of carefully chosen Bessel functions… 

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