Proof step e-6629899d205ea17b

basis_map A007318 → concludes about basis_map_A007318 of Triangle read by rows: row n consists of the nonzero coefficients of the expansion of 2^n x^n in terms of Hermite polynomials with decreas… JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A007318",
  "operation": "basis_map"
}

Premises

• Triangle read by rows: row n consists of the nonzero coefficients of the expansion of 2^n x^n in terms of Hermite polynomials with decreasi… (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" } } }
• { "claim": "interlacing", "from_index": 1, "kind": "weak", "orientation": "unordered" }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 c4fd82883b459db51bedaffe392b3e1c2a9d0efc0d031c0c8032d1ceb68ea296, 10,546 bytes (2,314 compressed); download JSON

Cited by

• n-87f3394ac59b064b (real_rooted)
• n-87f3394ac59b064b (one_signed_coefficients)
• n-87f3394ac59b064b (hadamard_kernel)
• n-87f3394ac59b064b (interlacing)