Proof step e-0adda7d4e180ead0

basis_map A013610 → concludes about basis_map_A013610 of Triangle T(n,k) read by rows: multiply row n of Pascal's triangle (A007318) by A001147(n). JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013610",
  "operation": "basis_map"
}

Premises

• Triangle T(n,k) read by rows: multiply row n of Pascal's triangle (A007318) by A001147(n). (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 b3bb6c4770534df3f7425d70f30f1930b59ccc260722d273a3035a5873d761f2, 7,419 bytes (1,629 compressed); download JSON

Cited by

• n-35f684e6e797bb02 (real_rooted)
• n-35f684e6e797bb02 (one_signed_coefficients)
• n-35f684e6e797bb02 (hadamard_kernel)