{
  "abstract": "We develop a hypergeometric framework for elliptic integral moments organized around Mishev's completed Saalschützian $L$-function and its $W(D_5)$ symmetry. The Bailey--Mishev very-well-poised ${}_7F_6(1)$ representation places complementary elliptic integral moments and harmonic hypergeometric sums in a common parameter space. We first give collision-based hypergeometric derivations of the three complementary-modulus moment families involving $K'^2$, $E'K'$, and $E'^2$. The $E'^2$ identity is also recovered independently from a Barnes-contiguous relation mirroring the differential system of the elliptic integrals. We then derive a hypergeometric evaluation of the harmonic-series representation of the four-Bessel moment $s_{4,0}$. At symmetric parameter points, Coxeter symmetry forces selected Taylor coefficients to vanish along symmetry-adapted paths, producing families of harmonic and special-value identities involving values of the Riemann zeta function and the same Bessel period. The resulting picture shows that these elliptic-moment, harmonic-sum, and special-value identities arise from a common $W(D_5)$ symmetry of generalized hypergeometric functions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.34016",
  "author_total": 1,
  "authors": [
    {
      "name": "Dianbin Bao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ek4rcd744fb1v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.34016",
  "fulltext_url": null,
  "id": "ek4rcd744fb1v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.34016",
  "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"
    ],
    [
      "arxiv",
      "math.NT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.34016",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ek4rcd744fb1v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.34016",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.34016"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Coxeter Symmetry in Hypergeometric Functions and Elliptic Integral Moments",
  "title_text": "Coxeter Symmetry in Hypergeometric Functions and Elliptic Integral Moments",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/ek4rcd744fb1v",
  "venue": "arXiv",
  "versions": []
}