Real-rooted atlas

Proof step

Affine, reversal and Möbius substitutions (elementary)

Image under a real-rootedness preserver affine, shift 0

Concludes
shift_x_plus_one of Triangle of coefficients of n!*(1 - x)^n*L_n(x/(1 - x)), where L_n(x) is the Laguerre polynomial.
Premises
Theorem
polytool ?
Lean
RealRooted Polynomial.Splits.comp_of_degree_le_one
Checked
polytool replayed · Lean not attempted
Technical details
Step id
e-f386eb84f6c9d238 · JSON
Operation
Image under a real-rootedness preserver
{
  "index_shift": 0,
  "operation": "preserver_image",
  "operator": "{\"shape\":\"affine\",\"slope\":\"1\",\"intercept\":\"1\"}"
}
Claims
{
  "claim": "real_rooted",
  "from_index": 1,
  "region": {
    "lower": {
      "closed": false,
      "value": "-1"
    },
    "upper": {
      "closed": false,
      "value": "0"
    }
  }
}
Certificate
preserver_image, SHA-256 96337b4ed5edce68626350421589b51115dba510063b7f385a62f2b5c2dee1c2, 16,448 bytes (2,860 compressed); download
polytool replayed the certificate when the step was written.
Cited by