{
  "id": "2402.11298",
  "version": "v1",
  "published": "2024-02-17T14:38:14.000Z",
  "updated": "2024-02-17T14:38:14.000Z",
  "title": "Clebsch-Gordan coefficients, hypergeometric functions and the binomial distribution",
  "authors": [
    "Jean-Christophe Pain"
  ],
  "categories": [
    "math-ph",
    "math.MP",
    "physics.atom-ph"
  ],
  "abstract": "A particular case of degenerate Clebsch-Gordan coefficient can be expressed with three binomial coefficients. Such a formula, which may be obtained using the standard ladder operator procedure, can also be derived from the Racah-Shimpuku formula or from expressions of Clebsch-Gordan coefficients in terms of $_3F_2$ hypergeometric functions. The O'Hara interesting interpretation of this Clebsch-Gordan coefficient by binomial random variables can also be related to hypergeometric functions ($_2F_1$), in the case where one of the parameters tends to infinity. This emphasizes the links between Clebsch-Gordan coefficients, hypergeometric functions and, what has been less exploited until now, the notion of probability within the framework of the quantum theory of angular momentum.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-02-17T14:38:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hypergeometric functions",
      "binomial distribution",
      "standard ladder operator procedure",
      "degenerate clebsch-gordan coefficient",
      "binomial random variables"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}