{
  "id": "1503.07897",
  "version": "v1",
  "published": "2015-03-25T14:25:13.000Z",
  "updated": "2015-03-25T14:25:13.000Z",
  "title": "Characterization of the Generalized Chebyshev Polynomials of First Kind",
  "authors": [
    "Mohammad A. AlQudah"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "Orthogonal polynomials have very useful properties in the solution of mathematical problems, so recent years have seen a great deal in the field of approximation theory using orthogonal polynomials. In this paper, we characterize the generalized Chebyshev orthogonal polynomials of the first kind $\\mathscr{T}_{n}^{(M,N)}(x),$ then we provide a closed form of the constructed polynomials in term of the Bernstein polynomials $B_{k}^{n}(x).$ We conclude the paper with some results on the integration of the product of the weighted generalized Chebyshev polynomials with the Bernstein polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-25T14:25:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C45",
      "42C05",
      "05A10",
      "33C60"
    ],
    "keywords": [
      "first kind",
      "bernstein polynomials",
      "characterization",
      "generalized chebyshev orthogonal polynomials",
      "great deal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150307897A"
    }
  }
}