Proof step e-89275777750acd05

basis_map A013609 → concludes about basis_map_A013609 of Triangle read by rows, T(n,k) = GegenbauerC(m,-n,-3/2) where m = k if k<n else 2*n-k, for n>=0 and 0<=k<=2n. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013609",
  "operation": "basis_map"
}

Premises

• Triangle read by rows, T(n,k) = GegenbauerC(m,-n,-3/2) where m = k if k<n else 2*n-k, for n>=0 and 0<=k<=2n. (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 06c24a7f44d6a721e12cc630ce3004a7b21a8309aa6ea8e3a9988678a15d5c1f, 6,877 bytes (1,394 compressed); download JSON

Cited by

• n-feae95e8ddee939b (real_rooted)
• n-feae95e8ddee939b (one_signed_coefficients)
• n-feae95e8ddee939b (hadamard_kernel)