{
  "abstract": "It is well-known that certain Möbius (linear fractional) transformations provide analytic continuation of the Gauss hypergeometric function. These transformations work by exchanging the roles of the three regular singular points and $0$, $1$, and $\\infty$ of the Gauss hypergeometric differential equation. Not one of these transformations, however, brings the points $e^{\\pm{\\rm i}π/3}$ closer to the origin, and convergence in a neighbourhood of these is also troublesome. In this work, we produce a Maclaurin series in optimal complexity after rational conformal mapping that induces pointwise convergence to any ${}_{q+1}F_q$ throughout the cut complex plane $\\mathbb{C}\\setminus[1,\\infty)$. We show that for the optimal parameter values this series converges faster than an approximate mapped Chebyshev series obtained by the ultraspherical spectral method.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35577",
  "author_total": 2,
  "authors": [
    {
      "name": "John Lopez"
    },
    {
      "name": "Richard Mikael Slevinsky"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dj1k9dn2v4q2a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35577",
  "fulltext_url": null,
  "id": "dj1k9dn2v4q2a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35577",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2604|Mathematical functions and polynomials"
    ]
  ],
  "openalex": "W7223946110",
  "pdf_url": "https://arxiv.org/pdf/2610.35577",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dj1k9dn2v4q2a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.35577",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35577"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Computing ${}_{q+1}{F}_q$ via rational conformal maps",
  "title_text": "Computing _q+1F_q via rational conformal maps",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/dj1k9dn2v4q2a",
  "venue": "arXiv",
  "versions": []
}