Proof step e-f67f09ded1c0d580

basis_map A013610 → concludes about basis_map_A013610 of Triangle whose (i,j)-th entry is binomial(i,j)*8^(i-j)*3^j. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013610",
  "operation": "basis_map"
}

Premises

• Triangle whose (i,j)-th entry is binomial(i,j)*8^(i-j)*3^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 40cab95f2a6a9d556c2c328c254cfe0de32089a1323cf4dc111b48ccf6ccabb6, 6,913 bytes (1,413 compressed); download JSON

Cited by

• n-4113d906b9d95b00 (real_rooted)
• n-4113d906b9d95b00 (one_signed_coefficients)
• n-4113d906b9d95b00 (hadamard_kernel)