{
  "abstract": "We analytically evaluate in terms of finite sums, the following definite improper integral, which appears in the quantum field theoretical calculation involving elementary charged particles having charge $\\pm e$ in presence of a constant external magnetic field $\\mathbf{B}=B\\hat{\\mathbf{z}}$ $$ I_{abln}^{μ_1\\dotsμ_r}(\\mathbf{q}_\\perp,|eB|) = \\int\\!\\!\\dfrac{d^2k_\\perp}{(2π)^2}k_\\perp^{μ_1} \\dots k_\\perp^{μ_r} \\exp \\bigg(-\\frac{\\mathbf{k}_\\perp^2+\\mathbf{p}_\\perp^2}{|eB|}\\bigg) L^a_l \\bigg(\\frac{2\\mathbf{k}_\\perp^2}{|eB|}\\bigg) L^b_n \\bigg(\\frac{2\\mathbf{p}_\\perp^2}{|eB|}\\bigg)\\bigg|_{\\mathbf{p}_\\perp=(\\mathbf{q}_\\perp+\\mathbf{k}_\\perp)} $$ where $μ_i \\in \\{1,2\\}$, $l\\ge 0$, $n\\ge 0$ and $L_l^a(x)$ are the generalized Laguerre polynomials. We also provide explicit expressions of the result up to the fourth moment i.e. $r=4$, which are sufficient for most of the field theoretical calculations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35995",
  "author_total": 1,
  "authors": [
    {
      "name": "Snigdha Ghosh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bmmhc2qqpjrx3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35995",
  "fulltext_url": null,
  "id": "bmmhc2qqpjrx3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35995",
  "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",
      "hep-ph"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2604|Mathematical functions and polynomials"
    ]
  ],
  "openalex": "W7224084288",
  "pdf_url": "https://arxiv.org/pdf/2610.35995",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bmmhc2qqpjrx3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:50Z",
      "native_id": "2610.35995",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35995"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-ph",
      "subfield": "high-energy"
    }
  ],
  "title": "Evaluation of a Double Integral with Exponentials and Two Generalized Laguerre Polynomials and Its Associated Moments",
  "title_text": "Evaluation of a Double Integral with Exponentials and Two Generalized Laguerre Polynomials and Its Associated Moments",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/bmmhc2qqpjrx3",
  "venue": "arXiv",
  "versions": []
}