Proof step e-e4ffd1425a5524fc

basis_map A038327 → concludes about Riordan array (1, 3+x). JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A038327",
  "operation": "basis_map"
}

Premises

• basis-map coefficients of Riordan array (1, 3+x). (sequence)
  uses: Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 12]

Claims

• { "claim": "real_rooted", "from_index": 1, "region": { "upper": { "closed": true, "value": "0" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 bc7817a6f36213ae580d96855e4a3db8cc1ef07e081379ef0f363e684a40a077, 11,704 bytes (2,211 compressed); download JSON

Cited by

• n-5d39164c4108e043 (hadamard_kernel)
• n-5d39164c4108e043 (real_rooted)
• n-5d39164c4108e043 (one_signed_coefficients)