{
  "abstract": "For a twice differentiable function $f:\\left( a,b\\right) \\rightarrow \\mathbb{R}$ define $v\\left( f\\right) =f^{\\prime}f^{\\prime}-f^{\\prime\\prime }f.$ It is well known that the positivity of $v\\left( f\\right) $ implies that the function $\\left\\vert f\\right\\vert $ is strictly log-concave on each subinterval which does not contain zeros of $f.$ In this paper we provide criteria for the positivity of $v\\left( F\\right) $ for the composite Bessel function $F\\left( x\\right) =J_{α,β,γ,ν}\\left( x\\right) :=x^αJ_ν\\left( βx^γ\\right) $ for positive numbers $β$ and $γ$ and real numbers $α$ and $ν.$",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11158",
  "author_total": 2,
  "authors": [
    {
      "name": "O. Kounchev"
    },
    {
      "name": "H. Render"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bd6cvpsncsdnv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11158",
  "fulltext_url": null,
  "id": "bd6cvpsncsdnv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11158",
  "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 Inequalities and Applications"
    ]
  ],
  "openalex": "W7212237326",
  "pdf_url": "https://arxiv.org/pdf/2609.11158",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bd6cvpsncsdnv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.11158",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11158"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "On the log-concavity of the composite Bessel function $x^αJ_{ν}\\left( βx^γ\\right) $",
  "title_text": "On the log-concavity of the composite Bessel function $x^αJ_{ν}\\left( βx^γ\\right) $",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/bd6cvpsncsdnv",
  "venue": "arXiv",
  "versions": []
}