Proof step e-99d5095ddb540cb3

basis_map A013609 → concludes about basis_map_A013609 of Coefficients of a special case of Poisson-Charlier polynomials. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013609",
  "operation": "basis_map"
}

Premises

• Coefficients of a special case of Poisson-Charlier polynomials. (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 04f8c4b334892b8a05b3a0567e2dbab7651994b58b28bacc7cba369c3ad5af44, 13,753 bytes (2,609 compressed); download JSON

Cited by

• n-95c4930a6d47b128 (real_rooted)
• n-95c4930a6d47b128 (one_signed_coefficients)
• n-95c4930a6d47b128 (hadamard_kernel)
• n-95c4930a6d47b128 (interlacing)