{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/investigation-into-the-role-of-the-bessel","title":"Investigation into the role of the Bessel function order in the Fourier-Bessel series and the Hankel Transform","arxiv_id":"2503.17722","date":"2025-03-22","proceeding":null,"authors":["Suketu P Patni","Vikram M Gadre"],"abstract":"This work focuses on estimating the number of terms of a Fourier-Bessel series of order $p'$ required to get within a certain error of a Bessel function of a fixed order $p$ where $p \\neq p'$. Our approach consists of two steps: one, constructing an invariant over $n$ of the $n^{\\text{th}}$ order Hankel transform; and two, observing the effect of expanding a suitably scaled Bessel function of a fixed order $p$ in its Fourier-Bessel series of order $p'$. We demonstrate a new error metric to simplify the error computations. Further, we generate an empirical model using numerical simulations and examine its capabilities in predicting the number of terms required.","url_abs":"https://arxiv.org/abs/2503.17722v1","url_pdf":"https://arxiv.org/pdf/2503.17722v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"investigation-into-the-role-of-the-bessel","repo_url":"https://github.com/suketu-patni/fourier_bessel_plots","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}