Proof step e-376f2b9433b6ff6b

basis_map A013611 → concludes about basis_map_A013611 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": "A013611",
  "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 37fc1ce920daf28f099d449e1b2ce1415cfe54683e7f743e97b22462352bfb40, 6,919 bytes (1,417 compressed); download JSON

Cited by

• n-a8292da3a4e72c99 (real_rooted)
• n-a8292da3a4e72c99 (one_signed_coefficients)
• n-a8292da3a4e72c99 (hadamard_kernel)