{"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/numerical-computation-of-stephenson-s-g","title":"Numerical computation of Stephenson's g-functions in multiply connected domains","arxiv_id":"2504.04629","date":"2025-04-06","proceeding":null,"authors":["Christopher C. Green","Mohamed M S Nasser"],"abstract":"There has been much recent attention on $h$-functions, so named since they describe the distribution of harmonic measure for a given multiply connected domain with respect to some basepoint. In this paper, we focus on a closely related function to the $h$-function, known as the $g$-function, which originally stemmed from questions posed by Stephenson in [3]. Computing the values of the $g$-function for a given planar domain and some basepoint in this domain requires solving a Dirichlet boundary value problem whose domain and boundary condition change depending on the input argument of the $g$-function. We use a well-established boundary integral equation method to solve the relevant Dirichlet boundary value problems and plot various graphs of the $g$-functions for different multiply connected circular and rectilinear slit domains.","url_abs":"https://arxiv.org/abs/2504.04629v1","url_pdf":"https://arxiv.org/pdf/2504.04629v1.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":"numerical-computation-of-stephenson-s-g","repo_url":"https://github.com/mmsnasser/gf","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}