{
  "id": "2502.00624",
  "version": "v1",
  "published": "2025-02-02T01:45:32.000Z",
  "updated": "2025-02-02T01:45:32.000Z",
  "title": "Expressing the difference of two Hurwitz zeta functions by a linear combination of the Gauss hypergeometric functions",
  "authors": [
    "Feng Qi"
  ],
  "comment": "12 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "In the paper, the author expresses the difference $2^m\\bigl[\\zeta\\bigl(-m,\\frac{1+x}{2}\\bigr)-\\zeta\\bigl(-m,\\frac{2+x}{2}\\bigr)\\bigr]$ in terms of a linear combination of the function $\\Gamma(m+1){\\,}_2F_1(-m,-x;1;2)$ for $m\\in\\mathbb{N}_0$ and $x\\in(-1,\\infty)$ in the form of matrix equations, where $\\Gamma(z)$, $\\zeta(z,\\alpha)$, and ${}_2F_1(a,b;c;z)$ stand for the classical Euler gamma function, the Hurwitz zeta function, and the Gauss hypergeometric function, respectively. This problem originates from the Landau level quantization in solid state materials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-02-02T01:45:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M35",
      "15A09",
      "33C05"
    ],
    "keywords": [
      "hurwitz zeta function",
      "gauss hypergeometric function",
      "linear combination",
      "difference",
      "solid state materials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}