{"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/on-the-function-describing-the-stellar","title":"On the function describing the stellar initial mass function","arxiv_id":"1212.0939","date":"2012-12-05","proceeding":null,"authors":["Thomas Maschberger"],"abstract":"We propose a functional form for the IMF, the L_3 IMF, which is a natural heavy-tailed approximation to the log-normal distribution. It is composed of a low-mass power law and a high mass power-law which are smoothly joined together. Three parameters are needed to achieve this. The standard IMFs of Kroupa-2001a, Kroupa-2002a and Chabrier-2003b (single stars or systems) are essentially indistinguishable from this form. Compared to other 3-parameter functions of the IMF, the L_3 IMF has the advantage that the cumulative distribution function and many other characteristic quantities have a closed form, the mass generating function, for example, can be written down explicitly.","url_abs":"https://arxiv.org/abs/1212.0939v1","url_pdf":"https://arxiv.org/pdf/1212.0939v1.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":"on-the-function-describing-the-stellar","repo_url":"https://github.com/asteca/imf","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}