Proof step

Geometric basis map (elementary)

Image under a basis map u^k -> P_k A013611

Concludes

Premises

shift_x_plus_one of Riordan array (1-x,x/(1-x)).
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]

Theorem

polytool ?

Checked

polytool replayed · Lean not attempted

Technical details

Step id

e-be00c68a27d32dae · JSON

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013611",
  "operation": "basis_map"
}

Claims

{
  "claim": "real_rooted",
  "from_index": 0,
  "region": {
    "upper": {
      "closed": true,
      "value": "0"
    }
  }
}

Certificate

basis_map, SHA-256 524f5ebcfdff6c388f6d0ab68c34d559aec25e0b3cf8c877246e865e293d8028, 6,899 bytes (1,402 compressed); download

polytool replayed the certificate when the step was written.

Cited by