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Complete Monotonicity of the Srivastava-Tomovski Function and Its Laplace-Wright Realization: Necessary and Sufficient Conditions — arXiv:2608.08198

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.08198
License (as archived): CC0-1.0
Archived: 2026-10-19T09:06:16.630Z
SHA-256 of the archived text: b19a76fafb97dfd7f53b0a71b5d59dcecbb1956e0105c20231106b9e028d2401
Stable URL of this page: https://metraipolis.com/documento/dc_dff589dda12e

How to cite

Complete Monotonicity of the Srivastava-Tomovski Function and Its Laplace-Wright Realization: Necessary and Sufficient Conditions — arXiv:2608.08198 — arXiv (en), https://arxiv.org/abs/2608.08198 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_dff589dda12e (Metraipolis archive dc_dff589dda12e, sha256 b19a76fafb97dfd7f53b0a71b5d59dcecbb1956e0105c20231106b9e028d2401)

BibTeX

@misc{dcdff589dda12e,
  title = {Complete Monotonicity of the Srivastava-Tomovski Function and Its Laplace-Wright Realization: Necessary and Sufficient Conditions — arXiv:2608.08198},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.08198},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_dff589dda12e; sha256 b19a76fafb97dfd7f53b0a71b5d59dcecbb1956e0105c20231106b9e028d2401},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.08198. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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 \(\Delta=1+\alpha-\kappa\). In the entire regime \(\Delta>0\), \(E_{\alpha,\beta}^{\gamma,\kappa}(-x)\) is completely monotone on \((0,\infty)\) if and only if \(\alpha\leq\kappa\) and \(\kappa\beta\geq\alpha\gamma\). For arbitrary positive parameters, the corresponding positive-axis realization satisfies the same criterion; when \(0<\alpha<\kappa\), 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 \(t\mapsto t^\kappa\) of a power-biased Wright distribution; at \(\alpha=\kappa\) it becomes a powered beta law for \(\beta>\gamma\) and the atom \(\Gamma(\gamma)^{-1}\delta_1\) for \(\beta=\gamma\). 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 \(\kappa=1\).

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-08-11 in math.ST).
Categorie arXiv: Statistics Theory (math.ST) ; Probability (math.PR).
Pagina del lavoro: https://arxiv.org/abs/2608.08198 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-19T09:04:01.353Z dalla pagina https://arxiv.org/catchup/math.ST/2026-08-11?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).