{
  "abstract": "Gosper introduced many remarkable formulas involving infinite products. One such formula provides an evaluation of the product $$\\prod_{n \\geq 1} \\frac{1}{e}\\left(\\frac{1}{3n} + 1\\right)^{3n + \\frac{1}{2}}. $$ It appears that a complete proof of this evaluation has not appeared in the literature. In this paper, we introduce some techniques to extend Gosper's evaluation. We prove a generalization of Gosper's formula involving three free parameters, which can also be applied to evaluate arbitrary multisections of Gosper's product. Then we investigate higher-order extensions involving higher-degree polynomials in $n$, relative to the polynomials $3n$ and $3n+\\frac{1}{2}$ involved in Gosper's product, yielding a generalization of an infinite product evaluation due to Ramanujan and recently studied by Bradley--Thrush [\\textit{\\it Ramanujan J.} (2025)]. We also consider connections with infinite products due to Kurokawa and Rovinski\\uı, building on the recent work of the first and fourth authors [\\textit{\\it Ramanujan J.} (2025)].",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03238",
  "author_total": 5,
  "authors": [
    {
      "name": "Jean-Paul Allouche"
    },
    {
      "name": "John M. Campbell"
    },
    {
      "name": "Simon R. Holcombe"
    },
    {
      "name": "Lubomir Markov"
    },
    {
      "name": "Manon Stipulanti"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/38m6km48fbp5p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03238",
  "fulltext_url": null,
  "id": "38m6km48fbp5p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03238",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Advanced Mathematical Identities"
    ]
  ],
  "openalex": "W7220461468",
  "pdf_url": "https://arxiv.org/pdf/2610.03238",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/38m6km48fbp5p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.03238",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03238"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Gosper's and Ramanujan's infinite products and generalizations",
  "title_text": "Gosper's and Ramanujan's infinite products and generalizations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/38m6km48fbp5p",
  "venue": "arXiv",
  "versions": []
}