{
  "abstract": "The asymptotic behavior of the coefficients of a sequence of polynomials is given under the conditions that all the zeros are real and positive and the zeros have an asymptotic zero distribution on $(0,\\infty)$. We show how the limit for the coefficients is related to the Stieltjes transform of the asymptotic zero distribution and make a connection with the $S$-transform in free probability. We illustrate with some examples involving orthogonal and multiple orthogonal polynomials.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12717",
  "author_total": 1,
  "authors": [
    {
      "name": "Walter Van Assche"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9vbzd6h5mkqaw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12717",
  "fulltext_url": null,
  "id": "9vbzd6h5mkqaw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12717",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CA"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2604|Mathematical functions and polynomials"
    ]
  ],
  "openalex": "W7212527028",
  "pdf_url": "https://arxiv.org/pdf/2609.12717",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9vbzd6h5mkqaw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.12717",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12717"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Asymptotics of the coefficients of polynomials, asymptotic zero distribution and free probability",
  "title_text": "Asymptotics of the coefficients of polynomials, asymptotic zero distribution and free probability",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/9vbzd6h5mkqaw",
  "venue": "arXiv",
  "versions": []
}