{
  "abstract": "We investigate higher-order $q$-difference equations obtained by successive applications of a $q$-analogue of addition and the $q$-middle convolution. We construct an $n$-dimensional system of linear $q$-difference equations and derive a single $q$-difference equation whose coefficients are polynomials of degree at most $1$ in the independent variable. Under certain conditions on the parameters, the resulting equation is a generalized $q$-hypergeometric equation of order $n$. We also obtain a multiple Jackson integral representation of solutions and give sufficient conditions for its convergence. By suitably choosing the functions appearing in the integrand and specializing the parameters, we obtain $q$-hypergeometric series solutions of type ${}_n ϕ_{n-1}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38286",
  "author_total": 1,
  "authors": [
    {
      "name": "Yumi Arai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/61a9gbs1t4fes.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38286",
  "fulltext_url": null,
  "id": "61a9gbs1t4fes",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38286",
  "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",
      "math.CA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38286",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/61a9gbs1t4fes.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38286",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38286"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "On $q$-middle convolution and generalized $q$-hypergeometric equation",
  "title_text": "On q-middle convolution and generalized q-hypergeometric equation",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/61a9gbs1t4fes",
  "venue": "arXiv",
  "versions": []
}