{
  "abstract": "We embed the Jacobi-like and Laguerre-like systems for ordinary type-I/type-II multiple orthogonality introduced by Wolfs into a single Askey-type confluence scheme. Applying the Bernstein transform simultaneously to the $q$ Jacobi-like weights produces a positive finite-lattice Hahn-like ancestor, represented by multiple beta integrals, reducing to the classical Hahn weight for $q=1$, and converging back to the continuous system. Parameter and scaling limits then yield Kravchuk-like, two Meixner-like, two Charlier-like, Jacobi-like, two Laguerre-like, and Hermite-like families. We realize every arrow through explicit hypergeometric orthogonality data. For each near-diagonal multi-index $1\\leq |\\mathbf m|\\leq N$, the Hahn-like type-II polynomial is a terminating ${}_{q+2}F_{q+1}(1)$ series satisfying an exact inverse Bernstein identity. We construct the normalized type-I form and, under explicit separation and nonvanishing assumptions, recover its individual polynomial components by finite sums of terminating hypergeometric functions and prove uniqueness. Finite-pole terms regroup into terminating Kampé de Fériet blocks. Their limits are obtained by coefficient extraction and reconstruction at infinity on the unreflected Kravchuk-like and Meixner-II-like branches, and by finite Lauricella--Horn sector sums on the reflected branches. This yields sectorwise component confluence along the Kravchuk--Charlier, Meixner--Charlier, Meixner--Laguerre, and Charlier--Hermite arrows. For $q=1$ all formulas reduce to the classical families; for $q>1$ the two Meixner-like systems, and likewise the two Charlier-like systems, are inequivalent under permutation of normalized rows.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08048",
  "author_total": 1,
  "authors": [
    {
      "name": "Manuel Mañas"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ez599pjxzprvk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08048",
  "fulltext_url": null,
  "id": "ez599pjxzprvk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08048",
  "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"
    ],
    [
      "openalex",
      "2604|Mathematical functions and polynomials"
    ]
  ],
  "openalex": "W7212047359",
  "pdf_url": "https://arxiv.org/pdf/2609.08048",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ez599pjxzprvk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.08048",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08048"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "An Askey-Type Confluence Scheme for Hahn-Like Multiple Orthogonality",
  "title_text": "An Askey-Type Confluence Scheme for Hahn-Like Multiple Orthogonality",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/ez599pjxzprvk",
  "venue": "arXiv",
  "versions": []
}