Proof step e-403803ced55fc794

basis_map A013611 → concludes about basis_map_A013611 of Triangle read by rows: T(n, k) is the Sheffer triangle ((1 - 4*x)^(-1/4), (-1/4)*log(1 - 4*x)). A generalized Stirling1 triangle. 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: T(n, k) is the Sheffer triangle ((1 - 4*x)^(-1/4), (-1/4)*log(1 - 4*x)). A generalized Stirling1 triangle. (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 2274450d102cb5a2f86cdaf71cd461959312521790562e3ddc911e911faaf930, 7,414 bytes (1,621 compressed); download JSON

Cited by

• n-fb74a9e290f1102e (real_rooted)
• n-fb74a9e290f1102e (one_signed_coefficients)
• n-fb74a9e290f1102e (hadamard_kernel)