Proof step e-3537980ff71b1a89

basis_map A007318 → concludes about A133080 * A007318. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• Interpolation operator: Triangle with an even number of zeros in each line followed by 1 or 2 ones. (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 1f22416e4c04fd46a184f046eff7ad157f40cb9dfd41bd12e1eab8e83366d34b, 6,925 bytes (1,400 compressed); download JSON

Cited by

• n-d75669a8cd7f9393 (real_rooted)
• n-d75669a8cd7f9393 (one_signed_coefficients)
• n-d75669a8cd7f9393 (hadamard_kernel)