{
  "abstract": "In this paper, by using a signs rule for a class of special power series and a recurrence relation of coefficients involving hypergeometric series, we find the necessary and sufficient conditions for the sharp (at the left endpoint) inequalities between the hypergeometric function and power mean (Hm-Pm inequality) to hold in all possible cases, which greatly extends those known results and solve the rest of problem on the sharp (at the left endpoint) power mean bounds for the hypergeometric mean.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10581",
  "author_total": 3,
  "authors": [
    {
      "name": "Zhen-Hang"
    },
    {
      "name": "Yang"
    },
    {
      "name": "Jing-Feng Tian"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b9b3e5pqp5rep.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10581",
  "fulltext_url": null,
  "id": "b9b3e5pqp5rep",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10581",
  "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.GM"
    ],
    [
      "openalex",
      "2604|Mathematical Inequalities and Applications"
    ]
  ],
  "openalex": "W7221182714",
  "pdf_url": "https://arxiv.org/pdf/2610.10581",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b9b3e5pqp5rep.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.10581",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10581"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GM",
      "subfield": "general"
    }
  ],
  "title": "The first type of power mean bounds for the Gaussian hypergeometric function",
  "title_text": "The first type of power mean bounds for the Gaussian hypergeometric function",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/b9b3e5pqp5rep",
  "venue": "arXiv",
  "versions": []
}