Proof step e-719615516772b132

basis_map A007318 → 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": "A007318",
  "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, 1]

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 0c60623b0d674a8c81ca0bd6dddf8ce7cca19e9af9509ad4715d42b020833e52, 11,588 bytes (2,153 compressed); download JSON

Cited by

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