Proof step e-5528cbe255a33964

basis_map A007318 → concludes about basis_map_A007318 of Riordan array (1, 3+x). JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• Riordan array (1, 3+x). (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 27cc9c48ac7a466b416fc946a856adcd3973771c97916dcf8d8972d6f833601b, 11,662 bytes (2,201 compressed); download JSON

Cited by

• n-a9307f854ca152e2 (real_rooted)
• n-a9307f854ca152e2 (one_signed_coefficients)
• n-a9307f854ca152e2 (hadamard_kernel)