### 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 |
---|---|

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 |

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### ASJC Scopus subject areas

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

### Cite this

*Journal of Physics A: Mathematical and General*,

*22*(21), 4729-4733. [033]. https://doi.org/10.1088/0305-4470/22/21/033

**A note on a series of Bessel functions : Asymptotic and convergence properties.** / Marksteiner, P.; Badralexe, E.; Freeman, Arthur J.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and General*, vol. 22, no. 21, 033, pp. 4729-4733. https://doi.org/10.1088/0305-4470/22/21/033

}

TY - JOUR

T1 - A note on a series of Bessel functions

T2 - Asymptotic and convergence properties

AU - Marksteiner, P.

AU - Badralexe, E.

AU - Freeman, Arthur J

PY - 1989

Y1 - 1989

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=36149032998&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36149032998&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/22/21/033

DO - 10.1088/0305-4470/22/21/033

M3 - Article

VL - 22

SP - 4729

EP - 4733

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 21

M1 - 033

ER -