Proof step e-b6c71ffc5380c303

basis_map A013609 → concludes about basis_map_A013609 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": "A013609",
  "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 9c318e551b0d141d13c960b020521b1f8ba5596cc52d7ca58c99247777489899, 11,956 bytes (2,342 compressed); download JSON

Cited by

• n-e7434b0161663b3b (real_rooted)
• n-e7434b0161663b3b (one_signed_coefficients)
• n-e7434b0161663b3b (hadamard_kernel)