### Abstract

A certain series of Bessel functions-recently discussed by Lee (1988)-is an asymptotic expansion of an integral of a Bessel function. Here the asymptotic properties of the series are investigated in more detail, and it is shown that the series is not only asymptotic, but also convergent under suitable restrictions. For large positive real arguments finite numbers of terms of the series give good approximations to the integral, but the infinite sum is different from the integral.

Original language | English |
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Article number | 033 |

Pages (from-to) | 4729-4733 |

Number of pages | 5 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 22 |

Issue number | 21 |

DOIs | |

Publication status | Published - 1989 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics

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## Cite this

Marksteiner, P., Badralexe, E., & Freeman, A. J. (1989). A note on a series of Bessel functions: Asymptotic and convergence properties.

*Journal of Physics A: Mathematical and General*,*22*(21), 4729-4733. [033]. https://doi.org/10.1088/0305-4470/22/21/033