Proof step e-7cc986a9eefcf6a5

basis_map A013609 → concludes about basis_map_A013609 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": "A013609",
  "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 39eb6ee994e53a67ac3ea1d832073bcead13a4f4eb668be4a8b7efb4c66d043f, 7,453 bytes (1,637 compressed); download JSON

Cited by

• n-578e4bbd7f77169d (real_rooted)
• n-578e4bbd7f77169d (one_signed_coefficients)
• n-578e4bbd7f77169d (hadamard_kernel)