Proof step e-849840c29c946dc7

basis_map A013610 → concludes about basis_map_A013610 of 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": "A013610",
  "operation": "basis_map"
}

Premises

• 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, 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 2b0cb5749b2e08d6a76baa16cec3b3849ccdd55fa3a9606bc077255367168aeb, 11,582 bytes (2,153 compressed); download JSON

Cited by

• n-d8e527df92e2a449 (real_rooted)
• n-d8e527df92e2a449 (one_signed_coefficients)
• n-d8e527df92e2a449 (hadamard_kernel)