Proof step e-0d5d22b8fd97251b

basis_map A013609 → concludes about basis_map_A013609 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": "A013609",
  "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 f401342399f9cd2d4af8ba418827cb8b2eb57f72216011cb8f47058c2bc8b401, 14,052 bytes (2,696 compressed); download JSON

Cited by

• n-820fbf6ab98121e9 (real_rooted)
• n-820fbf6ab98121e9 (one_signed_coefficients)
• n-820fbf6ab98121e9 (hadamard_kernel)
• n-820fbf6ab98121e9 (interlacing)