Proof step e-714d743cdbf8af98

basis_map A013610 → concludes about basis_map_A013610 of Square array read by antidiagonals downwards: T(n,k), n>=0, k>=0, in which column 0 is equal to A057427: 0, 1, 1, 1, ..., and for k > 0 co… JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• Square array read by antidiagonals downwards: T(n,k), n>=0, k>=0, in which column 0 is equal to A057427: 0, 1, 1, 1, ..., and for k > 0 col… (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 17f192fe9e4d6eb30431c15c344b85f9dc647aa2b6a6d2bae95b2b9fd82a1b89, 11,646 bytes (2,080 compressed); download JSON

Cited by

• n-2627c6fc0d9f64c9 (real_rooted)
• n-2627c6fc0d9f64c9 (one_signed_coefficients)
• n-2627c6fc0d9f64c9 (hadamard_kernel)