Proof step e-36015c56c1237184

basis_map A013610 → concludes about basis_map_A013610 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": "A013610",
  "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 2cab8e8391f1df5fe878b4d775bd0fd1c5e433e8cbedab7af9a961f71c2bf173, 7,453 bytes (1,637 compressed); download JSON

Cited by

• n-0d23d1c7119dd8ef (real_rooted)
• n-0d23d1c7119dd8ef (one_signed_coefficients)
• n-0d23d1c7119dd8ef (hadamard_kernel)