Proof step e-ce8b1eb4dfdacda9

basis_map A013611 → concludes about basis_map_A013611 of Riordan array (1, 3+x). JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013611",
  "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 28caaec43f4fc15a9f0c8cea69af8f8f02862f1a8c2cd457b262c816771f23b5, 11,666 bytes (2,201 compressed); download JSON

Cited by

• n-a6e4c21559f1b253 (real_rooted)
• n-a6e4c21559f1b253 (one_signed_coefficients)
• n-a6e4c21559f1b253 (hadamard_kernel)