Proof step e-6ef42593efb6357c

basis_map A013611 → concludes about basis_map_A013611 of basis-map coefficients of Riordan array (1+2x,x(1+x)). shifted by x -> -x + 0 JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013611",
  "operation": "basis_map"
}

Premises

• basis-map coefficients of Riordan array (1+2x,x(1+x)). shifted by x -> -x + 0 (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" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 2a2599c65c17bb7af737a12c3f6bde42e073d3a852fef4461b1eb9bb0b1e22f0, 6,865 bytes (1,391 compressed); download JSON

Cited by

• n-1e156f12069736a3 (real_rooted)
• n-1e156f12069736a3 (one_signed_coefficients)
• n-1e156f12069736a3 (hadamard_kernel)