Proof step e-d759043f254c4b9e

basis_map A013611 → concludes about basis_map_A013611 of Triangle read by rows: row n consists of n zeros followed by n!. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013611",
  "operation": "basis_map"
}

Premises

• Triangle read by rows: row n consists of n zeros followed by 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 db7704929cd20d235d149f27c0d3c2f5c1f65aea5eacd324c08dffd64594efd1, 7,409 bytes (1,615 compressed); download JSON

Cited by

• n-872d1ad8224c1da6 (real_rooted)
• n-872d1ad8224c1da6 (one_signed_coefficients)
• n-872d1ad8224c1da6 (hadamard_kernel)