Proof step e-e341175dbafd44bc

basis_map A013609 → concludes about basis_map_A013609 of 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": "A013609",
  "operation": "basis_map"
}

Premises

• Triangle of coefficients in expansion of (2+3x)^n. (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 1d307de01f7f614c7ea2cbb3056c71039d406028b78e2dc679de13389f99abe1, 6,855 bytes (1,394 compressed); download JSON

Cited by

• n-c1936dc488503f26 (real_rooted)
• n-c1936dc488503f26 (one_signed_coefficients)
• n-c1936dc488503f26 (hadamard_kernel)