{
  "id": "2109.11337",
  "version": "v1",
  "published": "2021-09-23T12:38:34.000Z",
  "updated": "2021-09-23T12:38:34.000Z",
  "title": "A modification of the Prudnikov and Laguerre polynomials",
  "authors": [
    "Semyon Yakubovich"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "A two-parameter sequence of orthogonal polynomials $\\{P_n( x; \\lambda, t)\\}_{n\\ge 0}$ with respect to the weight function $x^\\alpha e^{- \\lambda x} \\rho_\\nu(x t),\\ \\alpha > -1,\\ \\lambda, t \\ge 0, \\ \\rho_{\\nu}(x)= 2 x^{\\nu/2} K_\\nu(2\\sqrt x),\\ x >0, \\nu \\ge 0$, where $K_\\nu(z)$ is the modified Bessel function, is investigated. The case $\\lambda=0$ corresponds to the Prudnikov polynomials and $t=0$ is related to the Laguerre polynomials. A special one-parameter case $\\{P_n( x; 1-t, t)\\}_{n\\ge 0},\\ t \\in [0,1]$ is analyzed as well.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-23T12:38:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C47",
      "33C10",
      "44A15",
      "42C05"
    ],
    "keywords": [
      "laguerre polynomials",
      "modification",
      "special one-parameter case",
      "two-parameter sequence",
      "prudnikov polynomials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}