{
  "id": "math/0701345",
  "version": "v1",
  "published": "2007-01-12T13:37:02.000Z",
  "updated": "2007-01-12T13:37:02.000Z",
  "title": "Irrationality proof of certain Lambert series using little q-Jacobi polynomials",
  "authors": [
    "Jonathan Coussement",
    "Christophe Smet"
  ],
  "comment": "16 pages",
  "categories": [
    "math.CA",
    "math.NT"
  ],
  "abstract": "We apply the Pade technique to find rational approximations to % \\[h^{\\pm}(q_1,q_2)=\\sum_{k=1}^\\infty\\frac{\\q_1^k}{1\\pm \\q_2^k}, 0<q_1,q_2<1, q_1\\in\\mathbb{Q}, q_2=1/p_2, p_2\\in\\mathbb{N}\\setminus\\{1\\}.\\] % A separate section is dedicated to the special case $q_i=q^{r_i}, r_i\\in\\mathbb{N}, q=1/p, p\\in\\mathbb{N}\\setminus\\{1\\}$. In this construction we make use of little $q$-Jacobi polynomials. Our rational approximations are good enough to prove the irrationality of $h^{\\pm}(q_1,q_2)$ and give an upper bound for the irrationality measure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-01-12T13:37:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J72",
      "11J82",
      "33D45"
    ],
    "keywords": [
      "little q-jacobi polynomials",
      "lambert series",
      "irrationality proof",
      "rational approximations",
      "special case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......1345C"
    }
  }
}