Proof step e-9ff929e0a001a9a2

basis_map A013609 → concludes about basis_map_A013609 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": "A013609",
  "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 e196d2176eaccb208deb595e6b833923b0fde3fc7e3648cb7c52df9d6c6aea4a, 7,414 bytes (1,623 compressed); download JSON

Cited by

• n-de50e58c7c589630 (real_rooted)
• n-de50e58c7c589630 (one_signed_coefficients)
• n-de50e58c7c589630 (hadamard_kernel)