Proof step e-16890f4567488209

basis_map A007318 → concludes about basis_map_A007318 of Triangular array read by rows: row n gives the coefficients of the polynomial p(n,x) defined in Comments. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A007318",
  "operation": "basis_map"
}

Premises

• Triangular array read by rows: row n gives the coefficients of the polynomial p(n,x) defined in Comments. (sequence)
  uses: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]

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 67b785fe1a6bceca82cda5b2ec7d597f510e0e7fe8824b5e38b5ad015a97ec79, 11,956 bytes (2,338 compressed); download JSON

Cited by

• n-e7968148eadb4da9 (real_rooted)
• n-e7968148eadb4da9 (one_signed_coefficients)
• n-e7968148eadb4da9 (hadamard_kernel)