Proof step e-3771d6044a0ef815

basis_map A013611 → concludes about basis_map_A013611 of Riordan array ((1+x)/(1-2x),x(1+x)/(1-2x)). 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+x)/(1-2x),x(1+x)/(1-2x)). (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 ad61121c591232fa532480cf481dd94aa275d76d165dfda5ba7ceafecb2a58ee, 14,052 bytes (2,695 compressed); download JSON

Cited by

• n-2a476baf987bc613 (interlacing)
• n-2a476baf987bc613 (real_rooted)
• n-2a476baf987bc613 (one_signed_coefficients)
• n-2a476baf987bc613 (hadamard_kernel)