{
  "annotation_id": "17b6a2cd-af04-4371-ab7f-2ef2ef9ef716",
  "date_created": "2026-03-02T18:01:56.265000Z",
  "date_modified": "2026-03-02T18:01:56.265000Z",
  "file_hash": "c715b227cf153b3cab6b3f70728283d93918deb3531a937b3d4adf145e72e2b1",
  "private": false,
  "record": {
    "abstract": "We consider sequences of generalized Bell numbers B(n), n=0,1,... for which\nthere exist Dobinski-type summation formulas; that is, where B(n) is\nrepresented as an infinite sum over k of terms P(k)^n/D(k). These include the\nstandard Bell numbers and their generalizations appearing in the normal\nordering of powers of boson monomials, as well as variants of the \"ordered\"\nBell numbers. For any such B we demonstrate that every positive integral power\nof B(m(n)), where m(n) is a quadratic function of n with positive integral\ncoefficients, is the n-th moment of a positive function on the positive real\naxis, given by a weighted infinite sum of log-normal distributions.",
    "arxiv_id": "quant-ph/0303030",
    "authors": [
      "P. Blasiak",
      "K. A. Penson",
      "A. I. Solomon"
    ],
    "categories": [
      "quant-ph",
      "math.CO"
    ],
    "doi": "10.1088/0305-4470/36/18/101",
    "journal_ref": "J.Phys.A:Math.Gen. 36, L273 (2003)",
    "title": "Dobinski-type relations and the Log-normal distribution",
    "url": "https://arxiv.org/abs/quant-ph/0303030"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "5430fc2e-e5eb-4174-b1fe-008c85b7f8ca",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}