{
  "abstract": "We study two families of coefficients associated with powers of the tangent function and with products of the secant and tangent functions, and develop a unified treatment of the corresponding higher-order tangent and secant numbers. The first part establishes a common identity for even derivatives of $\\tanh x$ and odd derivatives of $\\operatorname{sech}x$. Combined with integral formulae for these derivatives, this yields finite power-integral representations for the normalized values $ζ(2n+1)$ and $β(2n)$ and naturally introduces two polynomial families $P_n$ and $Q_n$. We determine several arithmetic and structural properties of these polynomials. In particular, we identify the exact content of $P_n$, prove that $Q_n$ is primitive, establish strict log-concavity and unimodality of their coefficient sequences, and describe their real zeros. For even indices each family has a unique negative real zero, and the two sequences of real zeros have the same limit. We also derive differential recurrences and generating functions for $P_n$ and $Q_n$. The generating functions lead to a global complex-singularity analysis. We construct a compact Jordan curve $Γ$ and prove that the complex zero sets of both $P_n$ and $Q_n$ converge to $Γ$ in Hausdorff distance. The normalized zero-counting measures converge weakly to the same equilibrium measure on $Γ$. We determine the logarithmic capacity of the enclosed compact set, give an explicit arclength density for the limiting measure, and compute its first moments. Numerical plots for $P_{20}$, $P_{50}$, $P_{100}$ and $P_{150}$ illustrate the zero-attractor theorem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30208",
  "author_total": 1,
  "authors": [
    {
      "name": "Luc Ramsès Talla Waffo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/51ynzwdbafnke.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30208",
  "fulltext_url": null,
  "id": "51ynzwdbafnke",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30208",
  "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",
      "2602|Advanced Mathematical Identities"
    ]
  ],
  "openalex": "W7223323643",
  "pdf_url": "https://arxiv.org/pdf/2610.30208",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/51ynzwdbafnke.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.30208",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30208"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2602|Advanced Mathematical Identities",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Higher-order tangent and secant numbers, special-value integrals, and a common zero attractor",
  "title_text": "Higher-order tangent and secant numbers, special-value integrals, and a common zero attractor",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/51ynzwdbafnke",
  "venue": "arXiv",
  "versions": []
}