Proof step e-f0f6d4d5dc8cc42f

basis_map A007318 → concludes about shift_x_plus_one of 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

• A133080 * A007318. (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 9e7c97ccbe3671a2a0f66fc49f3e1cf44b621546ba0245c7664bd899204d8485, 6,925 bytes (1,403 compressed); download JSON

Cited by

• n-e5da0d00f07fcbc3 (one_signed_coefficients)
• n-e5da0d00f07fcbc3 (hadamard_kernel)
• n-e5da0d00f07fcbc3 (real_rooted)