A note on a series of Bessel functions: Asymptotic and convergence properties

P. Marksteiner; E. Badralexe; Arthur J Freeman

doi:10.1088/0305-4470/22/21/033

A note on a series of Bessel functions: Asymptotic and convergence properties

P. Marksteiner, E. Badralexe, Arthur J Freeman

Northwestern University

Research output: Contribution to journal › Article › peer-review

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	https://doi.org/10.1088/0305-4470/22/21/033
Publication status	Published - 1989

ASJC Scopus subject areas

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

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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.",

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