{
  "abstract": "In this paper, we establish an elementary functional identity \\begin{align*}\\sum_{k=1}^{n}\\bigg(\\frac{f(a,d_k)}{f(a,x)}\\bigg)^{n-1}\\prod_{i=1,i \\neq k}^{n} \\frac{g(x,d_i)}{g(d_k,d_i)}=1\\end{align*} based on a pair of functions $f(x, y)$ and $g(x,y)$ satisfying $$f(x, a) g(b, c)+f(x, b) g(c, a)+f(x, c) g(a, b)=0.$$ The latter may serve as a prototype for the classical Weierstrass theta identity. As a direct application, we establish a general transformation formula for finite sums. Some special algebraic, triangular and elliptic series transformations are also presented.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.27920",
  "author_total": 2,
  "authors": [
    {
      "name": "Jianan Xu"
    },
    {
      "name": "Qi Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8gjtgwmyj910f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.27920",
  "fulltext_url": null,
  "id": "8gjtgwmyj910f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.27920",
  "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.CA"
    ],
    [
      "openalex",
      "2602|Advanced Mathematical Identities"
    ]
  ],
  "openalex": "W7204805780",
  "pdf_url": "https://arxiv.org/pdf/2608.27920",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8gjtgwmyj910f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:28Z",
      "native_id": "2608.27920",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.27920"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Notices on a new functional identity and allied series transformations",
  "title_text": "Notices on a new functional identity and allied series transformations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:28Z",
  "url": "https://research.draconitic.com/paper/8gjtgwmyj910f",
  "venue": "arXiv",
  "versions": []
}