Proof step e-dab838a9194ad2c3

basis_map A013611 → concludes about basis_map_A013611 of Triangle whose (i,j)-th entry is binomial(i,j)*12^(i-j)*4^j. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• Triangle whose (i,j)-th entry is binomial(i,j)*12^(i-j)*4^j. (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 1358c6b079f5cc255e092ac95a8f7c9a4e61eb0640ebd7e7bbb0b984f34dc75e, 6,926 bytes (1,413 compressed); download JSON

Cited by

• n-b05662f2ce3af6a8 (real_rooted)
• n-b05662f2ce3af6a8 (one_signed_coefficients)
• n-b05662f2ce3af6a8 (hadamard_kernel)