{
  "id": "1409.1015",
  "version": "v1",
  "published": "2014-09-03T10:01:01.000Z",
  "updated": "2014-09-03T10:01:01.000Z",
  "title": "Special functions associated with positive linear operators",
  "authors": [
    "Ioan Rasa"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "Many well-known positive linear operators (like Bernstein, Baskakov, Sz\\'{a}sz-Mirakjan) are constructed by using specific fundamental functions. The sums of the squared fundamental functions have been objects of study in some recent papers. We investigate the relationship between these sums and some special functions. Consequently, we get integral representations and upper bounds for the sums. Moreover, we show that they are solutions to suitable second order differential equations. In particular, we provide polynomial or rational solutions to some Heun equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-03T10:01:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "special functions",
      "suitable second order differential equations",
      "specific fundamental functions",
      "well-known positive linear operators",
      "squared fundamental functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.1015R"
    }
  }
}