Proof step e-ef60f06c29a49051

basis_map A013609 → concludes about basis_map_A013609 of Riordan array (1/(1-2*x), x*(1+x)/(1-2*x)). JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013609",
  "operation": "basis_map"
}

Premises

• Riordan array (1/(1-2*x), x*(1+x)/(1-2*x)). (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" } } }
• { "claim": "interlacing", "from_index": 1, "kind": "weak", "orientation": "unordered" }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 4492f3cc0a15bc2356c22cab4c08ed5251b4f761b8b6525c40df27308e8d1f69, 14,052 bytes (2,695 compressed); download JSON

Cited by

• n-da6c9018f05787b2 (interlacing)
• n-da6c9018f05787b2 (real_rooted)
• n-da6c9018f05787b2 (one_signed_coefficients)
• n-da6c9018f05787b2 (hadamard_kernel)