{
  "id": "2006.11475",
  "version": "v1",
  "published": "2020-06-20T02:21:07.000Z",
  "updated": "2020-06-20T02:21:07.000Z",
  "title": "Zeros of a binomial combination of Chebyshev polynomials",
  "authors": [
    "Summer Al Hamdani",
    "Khang Tran"
  ],
  "categories": [
    "math.CA",
    "math.CV"
  ],
  "abstract": "For $0<\\alpha<1$, we study the zeros of the sequence of polynomials $\\left\\{ P_{m}(z)\\right\\} _{m=0}^{\\infty}$ generated by the reciprocal of $(1-t)^{\\alpha}(1-2zt+t^{2})$, expanded as a power series in $t$. Equivalently, this sequence is obtained from a linear combination of Chebyshev polynomials whose coefficients have a binomial form. We show that the number of zeros of $P_{m}(z)$ outside the interval $(-1,1)$ is bounded by a constant independent of $m$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-20T02:21:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30C15",
      "26C10",
      "11C08"
    ],
    "keywords": [
      "chebyshev polynomials",
      "binomial combination",
      "power series",
      "constant independent",
      "linear combination"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}