Real-rooted atlas

Proof step

Geometric basis map (elementary)

Image under a basis map u^k -> P_k A007318

Concludes
shift_x_plus_one of basis_map_A007318 of Triangle read by rows, T(n,k) = GegenbauerC(m,-n,-2) where m = k if k<n else 2*n-k, for n>=0 and 0<=k<=2n.
Premises
Theorem
polytool ?
Checked
polytool replayed · Lean not attempted
Technical details
Step id
e-d1668fb40a55d09f · JSON
Operation
Image under a basis map u^k -> P_k
{
  "map": "A007318",
  "operation": "basis_map"
}
Claims
{
  "claim": "real_rooted",
  "from_index": 0,
  "region": {
    "upper": {
      "closed": true,
      "value": "0"
    }
  }
}
Certificate
basis_map, SHA-256 36dddafbaf29b621c0063ef1fc54a166c8ccfc897f1026199503a8d9a9ad8ea2, 6,877 bytes (1,392 compressed); download
polytool replayed the certificate when the step was written.
Cited by