Proof step e-86b1b19edf92ec9a

basis_map A013609 → concludes about basis_map_A013609 of Triangle whose (i,j)-th entry is binomial(i,j)*3^(i-j)*3^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 whose (i,j)-th entry is binomial(i,j)*3^(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 556a0f5f49c75401805d6fd1ef61e3e2c76166403ff96f607996b6a0c4d0634a, 6,855 bytes (1,392 compressed); download JSON

Cited by

• n-0416b5b5a5f283f7 (real_rooted)
• n-0416b5b5a5f283f7 (one_signed_coefficients)
• n-0416b5b5a5f283f7 (hadamard_kernel)