Proof step

Geometric basis map (elementary)

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

Concludes

Premises

basis_map_A007318 of Riordan array (1/(1-2*x), x*(1+x)/(1-2*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-1f1ef648db1f4e2d · 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"
    }
  }
}

{
  "claim": "interlacing",
  "from_index": 1,
  "kind": "weak",
  "orientation": "unordered"
}

Certificate

basis_map, SHA-256 407674e2628e25fa3c640808109b15f0ec6d19e498453d5888811b3c6b00a068, 14,967 bytes (2,909 compressed); download

polytool replayed the certificate when the step was written.

Cited by