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Symmetry, Integrability and Geometry: Methods and Applications, 2018, Volume 14, 035, 13 pp.
DOI: https://doi.org/10.3842/SIGMA.2018.035
(Mi sigma1334)
 

This article is cited in 4 scientific papers (total in 4 papers)

On Basic Fourier–Bessel Expansions

José Luis Cardoso

Mathematics Department, University of Trás-os-Montes e Alto Douro (UTAD), Vila Real, Portugal
Full-text PDF (393 kB) Citations (4)
References:
Abstract: When dealing with Fourier expansions using the third Jackson (also known as Hahn–Exton) $q$-Bessel function, the corresponding positive zeros $j_{k\nu}$ and the “shifted” zeros, $qj_{k\nu}$, among others, play an essential role. Mixing classical analysis with $q$-analysis we were able to prove asymptotic relations between those zeros and the “shifted” ones, as well as the asymptotic behavior of the third Jackson $q$-Bessel function when computed on the “shifted” zeros. A version of a $q$-analogue of the Riemann–Lebesgue theorem within the scope of basic Fourier–Bessel expansions is also exhibited.
Keywords: third Jackson $q$-Bessel function; Hahn–Exton $q$-Bessel function; basic Fourier–Bessel expansions; basic hypergeometric function; asymptotic behavior; Riemann–Lebesgue theorem.
Funding agency Grant number
Fundação para a Ciência e a Tecnologia UID-MAT-00013/2013
This research was partially supported by FCT — Fundação para a Ciência e a Tecnologia, within the project UID-MAT-00013/2013.
Received: September 27, 2017; in final form April 11, 2018; Published online April 17, 2018
Bibliographic databases:
Document Type: Article
MSC: 42C10; 33D45; 33D15
Language: English
Citation: José Luis Cardoso, “On Basic Fourier–Bessel Expansions”, SIGMA, 14 (2018), 035, 13 pp.
Citation in format AMSBIB
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\paper On Basic Fourier--Bessel Expansions
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  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Symmetry, Integrability and Geometry: Methods and Applications
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