Proof step e-715b5f861d0b7004

basis_map A013609 → concludes about Triangle whose (i,j)-th entry is binomial(i,j)*3^(i-j)*2^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)*2^(i-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 65c5bca2723c4515024ec89af47e935c2b1da34050ec760a1ab1721bb0af924b, 6,855 bytes (1,390 compressed); download JSON

Cited by

• n-01cea33b6485d9cc (one_signed_coefficients)
• n-01cea33b6485d9cc (hadamard_kernel)
• n-01cea33b6485d9cc (real_rooted)