Proof step e-d7d2422771947afc

basis_map A013611 → concludes about basis_map_A013611 of Infinite lower triangular matrix with 2^k in the right diagonal and the rest zeros. Triangle, T(n,k), n zeros followed by the term 2^k. Tr… JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013611",
  "operation": "basis_map"
}

Premises

• Infinite lower triangular matrix with 2^k in the right diagonal and the rest zeros. Triangle, T(n,k), n zeros followed by the term 2^k. Tri… (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 4bd49e11c2cd67a80d8a5504cb5d586996302aea23e2332721cd4992f056a6d8, 6,855 bytes (1,391 compressed); download JSON

Cited by

• n-c96fe4c1be387a19 (real_rooted)
• n-c96fe4c1be387a19 (one_signed_coefficients)
• n-c96fe4c1be387a19 (hadamard_kernel)