Proof step e-e65e9efc7834c6f3

basis_map A013611 → concludes about basis_map_A013611 of Triangle read by rows: coefficients of the polynomials given by KummerU(-n, 1 - n - x, 3). JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013611",
  "operation": "basis_map"
}

Premises

• Triangle read by rows: coefficients of the polynomials given by KummerU(-n, 1 - n - x, 3). (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 952dc5e8f23a6f4b9e6af8798f08fe356709e85731c838abb5fc726ce750e11a, 13,431 bytes (2,546 compressed); download JSON

Cited by

• n-957f8e2516358b82 (real_rooted)
• n-957f8e2516358b82 (one_signed_coefficients)
• n-957f8e2516358b82 (hadamard_kernel)
• n-957f8e2516358b82 (interlacing)