Proof step e-dabb8392a3e47d84

basis_map A013609 → concludes about basis_map_A013609 of Triangle read by rows: T(n, k) is the Sheffer triangle ((1 - 3*x)^(-1/3), (-1/3)*log(1 - 3*x)). A generalized Stirling1 triangle. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013609",
  "operation": "basis_map"
}

Premises

• Triangle read by rows: T(n, k) is the Sheffer triangle ((1 - 3*x)^(-1/3), (-1/3)*log(1 - 3*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 c90be9a9328edb16122e2ba9701a924c1ddd449949c91e5bc71b18bc8b903e56, 7,414 bytes (1,622 compressed); download JSON

Cited by

• n-f1ff6363886186a4 (real_rooted)
• n-f1ff6363886186a4 (one_signed_coefficients)
• n-f1ff6363886186a4 (hadamard_kernel)