Proof step e-f9e5e2bc826d3dc0

basis_map A027465 → concludes about Riordan array (1+2x,x(1+x)). JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A027465",
  "operation": "basis_map"
}

Premises

• basis-map coefficients of Riordan array (1+2x,x(1+x)). (sequence)
  uses: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 3]

Claims

• { "claim": "real_rooted", "from_index": 0, "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 03d65c3b36ef224ccbffc98231f7410c4d8529acc804fef86c5653a689f11bfa, 11,591 bytes (2,162 compressed); download JSON

Cited by

• n-c27b11147fce8bfa (hadamard_kernel)
• n-c27b11147fce8bfa (real_rooted)
• n-c27b11147fce8bfa (one_signed_coefficients)