{"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/logolinear-series-expansions-with","title":"Logolinear series expansions with applications to primordial cosmology","arxiv_id":"1901.07540","date":"2019-01-21","proceeding":null,"authors":["Will Handley","Anthony Lasenby","Mike Hobson"],"abstract":"We develop a method for computing series expansions for solutions to ordinary differential equations when the asymptotic form contains both linear and logarithmic terms. Such situations are common in primordial cosmology when considering series expansions out of a singularity in the equations arising from a pre-inflationary phase of the universe. We develop mathematical techniques for generating these series expansions, and apply them to polynomial and Starobinsky inflationary potentials with kinetic initial conditions. Code for analytic and numerical computation of logolinear series is provided on GitHub.","url_abs":"http://arxiv.org/abs/1901.07540v2","url_pdf":"http://arxiv.org/pdf/1901.07540v2.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":"logolinear-series-expansions-with","repo_url":"https://github.com/williamjameshandley/logolinear","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}