[2005.06076] Discrete Bessel functions and transform Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematical Physics arXiv:2005.06076 (math-ph) [Submitted on 12 May 2020] Title: Discrete Bessel functions and transform Authors: Kenan Uriostegui , Kurt Bernardo Wolf View a PDF of the paper titled Discrete Bessel functions and transform, by Kenan Uriostegui and Kurt Bernardo Wolf View PDF HTML (experimental) Abstract: We present a straightforward discretization of the Bessel functions $J_n(x)$ to discrete counterparts $B^{(N)}_n(x_m)$, of $N$ integer orders $n$ on $N$ integer points $x_m \equiv m$, that we call discrete Bessel functions. These are built from a Bessel integral generating function, restricting the Fourier transform over the circle to $N$ points. We show that the discrete Bessel functions satisfy several linear and quadratic relations, particularly Graf's product-displacement formulas, that are exact analogues of well-known relations between the continuous functions. It is noteworthy that these discrete Bessel functions approximate very closely the values of the continuous functions in ranges $n + |m| < N$. For fixed $N$, this provides an $N$-point transform between functions of order and of position,$f_n$ and $\widetilde{f}_m$, which is efficient for the Fourier analysis of finite decaying signals. Comments: 11 pages, 3 figures Subjects: Mathematical Physics (math-ph) Cite as: arXiv:2005.06076 [math-ph] (or arXiv:2005.06076v1 [math-ph] for this version) https://doi.org/10.48550/arXiv.2005.06076 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Applied Mathematics & Information Sciences 15, No. 6, 1-8 (2021) Related DOI : https://doi.org/10.18576/amis/150606 Focus to learn more DOI(s) linking to related resources Submission history From: Kenan Uriostegui K. Uriostegui [ view email ] [v1] Tue, 12 May 2020 22:30:32 UTC (489 KB) Full-text links: Access Paper: View a PDF of the paper titled Discrete Bessel functions and transform, by Kenan Uriostegui and Kurt Bernardo Wolf View PDF HTML (experimental) TeX Source view license Current browse context: math-ph < prev | next > new | recent | 2020-05 Change to browse by: math math.MP References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from