{
  "abstract": "Two hypergeometric families of mixed-type multiple orthogonal forms are constructed for rank-one $q\\times p$ matrices of weights, with arbitrary $p$ and $q$: Jacobi and Laguerre I systems. Both normalized mixed forms are obtained explicitly for admissible near-diagonal multi-indices. The power-vector components are terminating generalized hypergeometric polynomials, while the hypergeometric-vector components are finite sums of such polynomials. In the Jacobi case, these sums are expressed as finite combinations of terminating Kampé de Fériet polynomials evaluated at $(x,1)$. For the mixed beta--Euler Laguerre I system, a finite triangular system relates the residues at finite poles to the terms generated by the Euler operator. Gamma-quotient Mellin formulas, Meijer $G$-representations, and Rodrigues formulas are derived for the complete mixed forms. On the step-line, the two biorthogonal systems satisfy dual recurrences governed by matrices with $p$ subdiagonals and $q$ superdiagonals. All recurrence coefficients are given by finite Gamma--Pochhammer expressions. Under normality and nonvanishing-pivot assumptions, Christoffel transformations and Gauss--Borel factorization yield bidiagonal factorizations of the recurrence matrices. The lower factors have closed Pochhammer formulas, while the upper factors are expressed through finite Christoffel tau-determinants or, equivalently, cross-ratios of shifted moment minors. Both Christoffel chains close explicitly in the mixed Piñeiro specialization.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.26110",
  "author_total": 1,
  "authors": [
    {
      "name": "Manuel Mañas"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/68eme1jtdv9hs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.26110",
  "fulltext_url": null,
  "id": "68eme1jtdv9hs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.26110",
  "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.CA"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2604|Mathematical functions and polynomials"
    ]
  ],
  "openalex": "W7214080672",
  "pdf_url": "https://arxiv.org/pdf/2609.26110",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/68eme1jtdv9hs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:11Z",
      "native_id": "2609.26110",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.26110"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Hypergeometric Mixed-Type Multiple Orthogonal Polynomials",
  "title_text": "Hypergeometric Mixed-Type Multiple Orthogonal Polynomials",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/68eme1jtdv9hs",
  "venue": "arXiv",
  "versions": []
}