{"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/2-fast-fast-and-accurate-computation-of","title":"2-FAST: Fast and accurate computation of projected two-point functions","arxiv_id":"1709.02401","date":"2017-09-07","proceeding":null,"authors":["Henry S. Grasshorn Gebhardt","Donghui Jeong"],"abstract":"We present the 2-point function from Fast and Accurate Spherical Bessel Transformation (2-FAST) algorithm for a fast and accurate computation of integrals involving one or two spherical Bessel functions. These types of integrals occur when projecting the galaxy power spectrum $P(k)$ onto the configuration space, $\\xi_\\ell^\\nu(r)$, or spherical harmonic space, $C_\\ell(\\chi,\\chi')$. First, we employ the FFTlog transformation of the power spectrum to divide the calculation into $P(k)$-dependent coefficients and $P(k)$-independent integrations of basis functions multiplied by spherical Bessel functions. We find analytical expressions for the latter integrals in terms of special functions, for which recursion provides a fast and accurate evaluation. The algorithm, therefore, circumvents direct integration of highly oscillating spherical Bessel functions.","url_abs":"https://arxiv.org/abs/1709.02401v3","url_pdf":"https://arxiv.org/pdf/1709.02401v3.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":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"2-fast-fast-and-accurate-computation-of","repo_url":"https://github.com/UnofficialJuliaMirror/TwoFAST.jl-0dd23c3e-f403-11e8-3e11-4dddf690af97","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"2-fast-fast-and-accurate-computation-of","repo_url":"https://github.com/UnofficialJuliaMirrorSnapshots/TwoFAST.jl-0dd23c3e-f403-11e8-3e11-4dddf690af97","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"2-fast-fast-and-accurate-computation-of","repo_url":"https://github.com/hsgg/TwoFAST.jl","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"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}