Proof step e-0566c972c7be0ca0

basis_map A007318 → concludes about basis_map_A007318 of Triangle read by rows: (i,j)-th entry is binomial(i,j)*3^(i-j)*8^j. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A007318",
  "operation": "basis_map"
}

Premises

• Triangle read by rows: (i,j)-th entry is binomial(i,j)*3^(i-j)*8^j. (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 736c23a88ba07e2d84138264ecd10152ceb482a5638ba2703d34a6b6cef115f9, 6,913 bytes (1,410 compressed); download JSON

Cited by

• n-2e0a8214849adcd6 (real_rooted)
• n-2e0a8214849adcd6 (one_signed_coefficients)
• n-2e0a8214849adcd6 (hadamard_kernel)