Proof step e-96071100df54473b

basis_map A013611 → concludes about basis_map_A013611 of Triangular array read by rows: row n gives the coefficients of the polynomial p(n,x) defined in Comments. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• Triangular array read by rows: row n gives the coefficients of the polynomial p(n,x) defined in Comments. (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 bd345aa3eafe0dc8814438086939c294999e3289ed7ee1f7152600ee0da905e6, 11,956 bytes (2,341 compressed); download JSON

Cited by

• n-8fa8f50d30f2716b (real_rooted)
• n-8fa8f50d30f2716b (one_signed_coefficients)
• n-8fa8f50d30f2716b (hadamard_kernel)