Proof step e-e9dcc990956c90e9

basis_map A013610 → concludes about Triangle of coefficients in expansion of (2+3x)^n. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013610",
  "operation": "basis_map"
}

Premises

• binomial (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 b9ad6e3f732c781faf8ff443521084dc4b58293ad6cdb552534bc8b81c811db0, 6,855 bytes (1,386 compressed); download JSON

Cited by

• n-5733d79f45a14084 (one_signed_coefficients)
• n-5733d79f45a14084 (hadamard_kernel)
• n-5733d79f45a14084 (real_rooted)