{
  "abstract": "Using the Andrews--Askey integral, we derive a holomorphic extension formula for a Jackson $q$-integral. This formula allows identities established for terminating specializations to be continued to the nonterminating case. Our first application yields two companion binomial-type double-sum formulas. The second formula contains, as special cases, the nonterminating Sears--Carlitz transformation of Gasper and Rahman and Rahman's generating function for the Askey--Wilson polynomials. Applying the same method to the $q$-Chu--Vandermonde and Rogers' ${}_6ϕ_5$ summations, we obtain two further integral representations for double sums of basic hypergeometric type. A balanced ${}_4ϕ_3$ specialization of the latter identity is equivalent, via Sears' transformation, to the double-series transformation of Ismail, Rahman, and Suslov.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00074",
  "author_total": 1,
  "authors": [
    {
      "name": "Takumi Maesaka"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8a4mwp4xbysb4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00074",
  "fulltext_url": null,
  "id": "8a4mwp4xbysb4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00074",
  "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.CO"
    ],
    [
      "openalex",
      "2604|Mathematical functions and polynomials"
    ]
  ],
  "openalex": "W7206157667",
  "pdf_url": "https://arxiv.org/pdf/2609.00074",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8a4mwp4xbysb4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2609.00074",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00074"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Double basic hypergeometric sums via a regularized Jackson $q$-integral",
  "title_text": "Double basic hypergeometric sums via a regularized Jackson q-integral",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/8a4mwp4xbysb4",
  "venue": "arXiv",
  "versions": []
}