Proof step e-d2b5f968b40c2621

basis_map A013610 → concludes about basis_map_A013610 of Triangle whose (n,k)-th entry is 15^(n-k)*binomial(n,k). JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• Triangle whose (n,k)-th entry is 15^(n-k)*binomial(n,k). (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 203b9083513372da911b992dfaee7091676f81ad445520d8e3359dfbbdf8d75e, 6,860 bytes (1,390 compressed); download JSON

Cited by

• n-16c98a2b049669c5 (real_rooted)
• n-16c98a2b049669c5 (one_signed_coefficients)
• n-16c98a2b049669c5 (hadamard_kernel)