{
  "abstract": "We determine necessary and sufficient conditions for complete monotonicity of the Srivastava--Tomovski extension, a generalized Mittag--Leffler kernel arising in fractional calculus, while separating the defining generalized-Wright series from its positive-axis realization when the series is not entire. For positive parameters, let \\(Δ=1+α-κ\\). In the entire regime \\(Δ>0\\), \\(E_{α,β}^{γ,κ}(-x)\\) is completely monotone on \\((0,\\infty)\\) if and only if \\(α\\leqκ\\) and \\(κβ\\geqαγ\\). For arbitrary positive parameters, the corresponding positive-axis realization satisfies the same criterion; when \\(0<α<κ\\), it is defined by a second-kind Wright kernel and remains meaningful through the finite-radius and zero-radius phases of the defining series. We also identify the Bernstein measure in every admissible case. In the interior region it is, after normalization, the pushforward under \\(t\\mapsto t^κ\\) of a power-biased Wright distribution; at \\(α=κ\\) it becomes a powered beta law for \\(β>γ\\) and the atom \\(Γ(γ)^{-1}δ_1\\) for \\(β=γ\\). Necessity in the excluded regions follows from a Mellin-transform zero, uniqueness of finite signed Laplace transforms, and moment-support asymptotics. The Prabhakar criterion is recovered by setting \\(κ=1\\).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.08198",
  "author_total": 3,
  "authors": [
    {
      "name": "Rey R. Cuenca"
    },
    {
      "name": "Welfredo R. Patungan"
    },
    {
      "name": "Ruzzel Ragas"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ad6dw5szj91vw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.08198",
  "fulltext_url": null,
  "id": "ad6dw5szj91vw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.08198",
  "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.PR"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2604|Mathematical Inequalities and Applications"
    ]
  ],
  "openalex": "W7202185979",
  "pdf_url": "https://arxiv.org/pdf/2608.08198",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ad6dw5szj91vw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2608.08198",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.08198"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Complete Monotonicity of the Srivastava-Tomovski Function and Its Laplace-Wright Realization: Necessary and Sufficient Conditions",
  "title_text": "Complete Monotonicity of the Srivastava-Tomovski Function and Its Laplace-Wright Realization: Necessary and Sufficient Conditions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:22Z",
  "url": "https://research.draconitic.com/paper/ad6dw5szj91vw",
  "venue": "arXiv",
  "versions": []
}