Proof step e-a33c0ab38a356260

basis_map A007318 → concludes about basis_map_A007318 of Unsigned 2-Stirling numbers of the first kind. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• Unsigned 2-Stirling numbers of the first kind. (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" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 da3e2c8f57b98a796053f5e39a4fa85a835b7d9555df6952d176ff8e93d195a6, 7,451 bytes (1,630 compressed); download JSON

Cited by

• n-1b45c74901cc1e95 (real_rooted)
• n-1b45c74901cc1e95 (one_signed_coefficients)
• n-1b45c74901cc1e95 (hadamard_kernel)