Proof step e-c8a2ee9cf24a53ed

basis_map A013609 → concludes about basis_map_A013609 of Triangle read by rows: (i,j)-th entry is binomial(i,j)*3^(i-j)*8^j. 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: (i,j)-th entry is binomial(i,j)*3^(i-j)*8^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 c89d5c5ac5fed2f9770ccacc5fd72e30f5c976f50f5fb964ef93c146d46246c9, 6,917 bytes (1,419 compressed); download JSON

Cited by

• n-1600c9e1b40ceecc (real_rooted)
• n-1600c9e1b40ceecc (one_signed_coefficients)
• n-1600c9e1b40ceecc (hadamard_kernel)