{
  "abstract": "Let $η\\geq 0$ and $δ>0$, and let $(r_j)_{j\\geq 0}$ be a sequence of real numbers satisfying $η\\leq r_0 < r_1 < r_2 < \\cdots$ and $r_{j+1}-r_j \\geq δ$ for every $j\\geq 0$. We prove that, for $δ\\leq 1$ and every $x>0$, \\[ \\sum_{j=0}^\\infty \\frac{x^{r_j}}{\\G(1+r_j)} \\leq \\sum_{j=0}^\\infty \\frac{x^{η+jδ}}{\\G(1+η+jδ)} = x^ηE_{δ,1+η}(x^δ), \\] where $E_{δ,1+η}$ denotes the two-parameter Mittag-Leffler function. Moreover, equality holds for some $x>0$ if and only if $r_j = η+ jδ$ for every $j$. The proof combines a finite compression argument for unimodal functions with a shift inequality for the Mittag-Leffler function. The upper bound $δ\\leq 1$ is sharp, since counterexamples exist for every $1 < δ< 2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.04540",
  "author_total": 1,
  "authors": [
    {
      "name": "Giuseppe Molteni"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0qfwwpsfa63q5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.04540",
  "fulltext_url": null,
  "id": "0qfwwpsfa63q5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.04540",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.04540",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0qfwwpsfa63q5.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.04540",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.04540"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A sharp Mittag-Leffler bound for series with separated exponents",
  "title_text": "A sharp Mittag-Leffler bound for series with separated exponents",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/0qfwwpsfa63q5",
  "venue": "arXiv",
  "versions": []
}