{
  "annotation_id": "b53b4657-0b86-4382-915a-baae4615f8ed",
  "date_created": "2026-02-17T05:53:23.785000Z",
  "date_modified": "2026-02-17T05:53:23.785000Z",
  "file_hash": "2a0335b396ff3092a26ccb36a28a731c511e5355c770b1dc6f4c2f1918d15e6d",
  "private": false,
  "record": {
    "abstract": "For $a,b,c,z,p, \\theta \\in \\mathbb{C}$, where $\\mathbb{C}$ is the complex plane, $-c\\notin \\mathbb{N\\cup }\\left\\{ 0\\right\\} $, let \\begin{equation*} \\mathcal{M}\\left( z\\right) =\\left( 1-\\theta z\\right) ^{p}M\\left(a;c;z\\right) =\\sum_{n=0}^{\\infty }u_{n}z^{n}, \\end{equation*} where $|z| \u003c\\frac{1}{\\theta}$, $|\\arg (1-\\theta z)| \u003c \\pi$, and let \\begin{equation*} \\mathcal{G}\\left( z\\right) =(1-\\theta z) ^{p}F(a,b;c;z) =\\sum_{n=0}^{\\infty }v_{n} z^{n}, \\end{equation*} where $|z| \u003c 1$, $|\\arg (1-\\theta z)| \u003c \\pi$. In this paper, we prove that the coefficients $u_{n}$ and $v_{n}$ for $n\\geq 0$ satisfy a 3-order recurrence relation. These offer a new way to study confluent hypergeometric function $M(a;c;z)$ and Gauss hypergeometric function $F(a,b;c;z)$. And we provide other special functions\u0027 recurrence relations of their coefficients, such as error function, Bessel function, incomplete gamma function, complete elliptic integral and Chebyshev polynomials.",
    "arxiv_id": "2601.10040",
    "authors": [
      "Zi-Qiao Xu",
      "Zhong-Xuan Mao",
      "Jing-Feng Tian"
    ],
    "categories": [
      "math.CV",
      "math.CA"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "title": "Recurrence relations for the coefficients of the confluent and Gauss hypergeometric functions in the complex plane",
    "url": "https://arxiv.org/abs/2601.10040",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ad291df6-b4d8-4930-a399-ea903da2fc91",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}