Real-rooted atlas

Proof step

Affine, reversal and Möbius substitutions (elementary)

Image under a real-rootedness preserver mobius, shift 0

Concludes
mobius_x_over_x_plus_one of Triangle of coefficients of Chebyshev's S(n,x+5) polynomials (exponents of x in increasing order).
Premises
Theorem
polytool ?
Lean
RealRooted route fTransform RealRooted.splits_fPolynomial
Checked
polytool replayed · Lean not attempted
Technical details
Step id
e-176dcc9e47e34f2d · JSON
Operation
Image under a real-rootedness preserver
{
  "index_shift": 0,
  "operation": "preserver_image",
  "operator": "{\"shape\":\"mobius\",\"a\":\"1\",\"b\":\"0\",\"c\":\"1\",\"e\":\"1\",\"schedule\":{\"first_index\":0,\"first_degree\":0,\"step\":1}}"
}
Claims
{
  "claim": "real_rooted",
  "from_index": 0,
  "region": {
    "lower": {
      "closed": true,
      "value": "-1"
    },
    "upper": {
      "closed": false,
      "value": "-3/4"
    }
  }
}
Certificate
preserver_image, SHA-256 c0f7ec4a330d6ca51d6555360f4399b98f40cae9f047741f802fbd6fb82932e4, 17,615 bytes (3,487 compressed); download
polytool replayed the certificate when the step was written.
Cited by