Proof step e-78e814d9774691df

basis_map A007318 → concludes about basis_map_A007318 of Triangle read by rows: T(n,k) are the coefficients of Charlier polynomials: A046716 transposed, for 0 <= k <= n. 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: T(n,k) are the coefficients of Charlier polynomials: A046716 transposed, for 0 <= k <= n. (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" } } }
• { "claim": "interlacing", "from_index": 2, "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 d5016775691e3532fcc79a6221d087f9c80e1fc2975631b91c573e7bb4bca3bf, 13,430 bytes (2,535 compressed); download JSON

Cited by

• n-8addbc07b5fd134f (real_rooted)
• n-8addbc07b5fd134f (one_signed_coefficients)
• n-8addbc07b5fd134f (hadamard_kernel)
• n-8addbc07b5fd134f (interlacing)