Proof step e-532ccda39f04a0f0

basis_map A038303 → 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": "A038303",
  "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, 10]

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 f6ff3b8d6ab0d4da0a06173c07812c30d8dfd364a51763d811734ab2025c5d74, 11,703 bytes (2,189 compressed); download JSON

Cited by

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