On Fourier–Bessel series and the Kneser–Sommerfeld expansion

descriptionPublicationkeyboard_double_arrow_right Article 09 Oct 2021 English Publisher:WileyJournal:Mathematical Methods in the Applied Sciences, volume 45, pages 1,145-1,152 (issn: 0170-4214, eissn: 1099-1476,

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Authors: P.A. Martin;

doi: 10.1002/mma.7841

On Fourier–Bessel series and the Kneser–Sommerfeld expansion

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Abstract

An error in Watson's Bessel Functions is corrected. It concerns a certain Fourier–Bessel series, an infinite series in which the terms involve the zeros of a Bessel function. Several related examples are discussed, and a connection with finite‐part integrals is noted.

Related Organizations

Colorado School of Mines
United States

Keywords

Bessel functions, special functions, Fourier coefficients, Fourier series of functions with special properties, special Fourier series, Fourier-Bessel series, Bessel and Airy functions, cylinder functions, \({}_0F_1\), finite-part integrals

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