Proof step e-48de33f15b8f0da9

basis_map A007318 → concludes about shift_x_plus_one of Riordan array (1+2x,x(1+x)). JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• Riordan array (1+2x,x(1+x)). (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 8e495bac03e4a2b90dd8ad398258aab0d45018a16fb88ba9280317fc2bca2254, 11,582 bytes (2,150 compressed); download JSON

Cited by

• n-fb2cd7d8c683bee9 (one_signed_coefficients)
• n-fb2cd7d8c683bee9 (hadamard_kernel)
• n-fb2cd7d8c683bee9 (real_rooted)