Proof step e-85e8843cd1dca083

basis_map A013610 → concludes about basis_map_A013610 of Triangle whose (i,j)-th entry is binomial(i,j)*12^(i-j)*12^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)*12^(i-j)*12^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 d2dcc4a9b3f82ab81fc655b0de451c687c3e5bcbd200fa9f1090518503324d8c, 6,939 bytes (1,424 compressed); download JSON

Cited by

• n-67e5bcee85c7fcd9 (real_rooted)
• n-67e5bcee85c7fcd9 (one_signed_coefficients)
• n-67e5bcee85c7fcd9 (hadamard_kernel)