Proof step e-d06691736a5246b1

basis_map A007318 → concludes about basis_map_A007318 of Triangle whose (i,j)-th entry is binomial(i,j)*12^(i-j)*1^j. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A007318",
  "operation": "basis_map"
}

Premises

• Triangle whose (i,j)-th entry is binomial(i,j)*12^(i-j)*1^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 d7f76e7c1d583673fc5af3d763b46663278887dd4a9375691c8368b17bf50417, 6,860 bytes (1,385 compressed); download JSON

Cited by

• n-7a809bc95dc4396c (one_signed_coefficients)
• n-7a809bc95dc4396c (hadamard_kernel)
• n-7a809bc95dc4396c (real_rooted)