Proof step e-eea0c95a12d0633a

basis_map A013609 → concludes about basis_map_A013609 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": "A013609",
  "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 b670e795d0fe48338e695a0a6071c0b82975f71428dcdb4fc55c465fc69741a5, 7,409 bytes (1,616 compressed); download JSON

Cited by

• n-439ac61e3f209ac0 (real_rooted)
• n-439ac61e3f209ac0 (one_signed_coefficients)
• n-439ac61e3f209ac0 (hadamard_kernel)