Proof step e-b4660546a5e77fa6

basis_map A013609 → concludes about basis_map_A013609 of Triangle: row #n has n+1 terms. T(n,m) = 4^m (2n+1)! / ( (2n-2m)! (2m+1)! ). JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013609",
  "operation": "basis_map"
}

Premises

• Triangle: row #n has n+1 terms. T(n,m) = 4^m (2n+1)! / ( (2n-2m)! (2m+1)! ). (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" } } }
• { "claim": "interlacing", "from_index": 1, "kind": "weak", "orientation": "unordered" }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 7e87555fc07ee280a064397613bb96909e70a605ccce69c93fdabd2bdc590359, 13,663 bytes (2,603 compressed); download JSON

Cited by

• n-393cac5827041b9e (real_rooted)
• n-393cac5827041b9e (one_signed_coefficients)
• n-393cac5827041b9e (hadamard_kernel)
• n-393cac5827041b9e (interlacing)