On the convergence of the expansion of an arbitrary function \(f(x)\) in terms of the Bessel functions \[ J^{a}(\beta x), \; J^{a}(\beta_{2}x), \; J^{a}(\beta_{3}x), \ldots , \] where \(\beta_{1}, \beta_{2}, \beta_{3}, \ldots\) are the positive roots of
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Publication:5969802
DOI10.1007/BF01442456zbMath08.0310.02OpenAlexW239021743MaRDI QIDQ5969802
Publication date: 1876
Published in: Mathematische Annalen (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf01442456
Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10)
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