{
  "abstract": "We study the monic recurrence coefficients of the generalized Charlier polynomials associated with the discrete weight \\[ ρ_μ(k) = \\frac{μ^k}{(k!)^2}, \\qquad k\\in\\mathbb N_0, \\qquad μ>0. \\] The coefficients $β_n$ and $γ_n$ in the recurrence relation \\[ P_{n+1}(x) = (x-β_n)P_n(x)-γ_nP_{n-1}(x) \\] are described through complementary moment, determinant, discrete dynamical, and continuous integrable formulations. We give a consistent normalization of the Markov function and its Jacobi continued fraction, and express the recurrence coefficients in terms of Hankel determinants, using a bordered determinant for the diagonal coefficient $β_n$. Starting from the original Laguerre--Freud equations, we derive the local recursive system used for computation and relate it to the Toda deformation. We also recall the known Painlevé~V representations associated with the two-parameter generalized Charlier family, in a normalization consistent with the present specialization. Moment/Hankelconstructions provide complementary moment-theoretic realizations of the recurrence coefficients, while the local Laguerre--Freud recursion provides an independent dynamical construction. Their comparison is used for numerical cross-validation. The numerical results are consistent with the leading large-degree behavior \\[ β_n\\sim n, \\qquad γ_n\\simμ. \\]",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35895",
  "author_total": 1,
  "authors": [
    {
      "name": "Mahouton Norbert Hounkonnou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fz0xtpnsspzby.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35895",
  "fulltext_url": null,
  "id": "fz0xtpnsspzby",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35895",
  "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-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "nlin.SI"
    ],
    [
      "openalex",
      "2604|Mathematical functions and polynomials"
    ]
  ],
  "openalex": "W7214940786",
  "pdf_url": "https://arxiv.org/pdf/2609.35895",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fz0xtpnsspzby.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:31Z",
      "native_id": "2609.35895",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35895"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:nlin.SI",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Generalized Charlier Recurrence Coefficients: Hankel Formulas, Laguerre--Freud Dynamics, and Painlevé V Connections",
  "title_text": "Generalized Charlier Recurrence Coefficients: Hankel Formulas, Laguerre--Freud Dynamics, and Painlevé V Connections",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/fz0xtpnsspzby",
  "venue": "arXiv",
  "versions": []
}