Proof step e-af79ef336fd9f8da

basis_map A027465 → concludes about Riordan array (1, 2+2x). JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A027465",
  "operation": "basis_map"
}

Premises

• basis-map coefficients of Riordan array (1, 2+2x). (sequence)
  uses: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 3]

Claims

• { "claim": "real_rooted", "from_index": 0, "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 cd653b202d69c8f546dce01fa0ddbc7ce54fa71c4c8ac29cedb290ba505b9b27, 11,670 bytes (2,197 compressed); download JSON

Cited by

• n-f5a001953ee28e8f (one_signed_coefficients)
• n-f5a001953ee28e8f (hadamard_kernel)
• n-f5a001953ee28e8f (real_rooted)