Proof step e-d82776c4e84d5954

basis_map A007318 → concludes about shift_x_plus_one of basis-map coefficients of A scaled Hermite triangle. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• basis-map coefficients of A scaled Hermite triangle. (sequence)
  uses: Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 0]

Claims

• { "claim": "real_rooted", "from_index": 1, "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 98c24a8ac688332f0615cc216129eefbdaa1e69f9e18e97d8f1bb13e2c79ef83, 6,895 bytes (1,399 compressed); download JSON

Cited by

• n-dd649f176537f8e7 (one_signed_coefficients)
• n-dd649f176537f8e7 (hadamard_kernel)
• n-dd649f176537f8e7 (real_rooted)