Proof step e-2d0268d4f6f3cbee

basis_map A038291 → 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": "A038291",
  "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, 9]

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 2925d757db9c248799ea2b821ba61a02926e3c46bfa225b810e0066aa3a6166f, 11,677 bytes (2,208 compressed); download JSON

Cited by

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