Proof step e-33def10999a9e794

basis_map A013610 → concludes about basis_map_A013610 of basis-map coefficients of A scaled Hermite triangle. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013610",
  "operation": "basis_map"
}

Premises

• basis-map coefficients of A scaled Hermite triangle. (sequence)
  uses: Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 0]

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 096b57d8a3757d7aa48128ba88fc7b0ff5cccaa14deedd669198dfed9b6a9a51, 6,895 bytes (1,400 compressed); download JSON

Cited by

• n-b8d8f9de0e27e805 (real_rooted)
• n-b8d8f9de0e27e805 (one_signed_coefficients)
• n-b8d8f9de0e27e805 (hadamard_kernel)