Proof step e-f5d1118e248686fe

basis_map A013609 → concludes about basis_map_A013609 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": "A013609",
  "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 c89deb1a681c2118fcfe1d77cb198917dddb17c96fcf2f8179eb94d683a45b9a, 10,546 bytes (2,319 compressed); download JSON

Cited by

• n-6fd4325317ef314b (real_rooted)
• n-6fd4325317ef314b (one_signed_coefficients)
• n-6fd4325317ef314b (hadamard_kernel)
• n-6fd4325317ef314b (interlacing)