Proof step e-af828196d3a769ca

basis_map A007318 → concludes about shift_x_plus_one of basis-map coefficients of Riordan array (1+2x,x(1+x)). shifted by x -> -x + 0 JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• basis-map coefficients of Riordan array (1+2x,x(1+x)). shifted by x -> -x + 0 (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 e382c601d8274eafa06041ea4ebd52a3244f6e37a355d796ef2e20d7b1ec7deb, 6,865 bytes (1,387 compressed); download JSON

Cited by

• n-f8c9dbb903f44fdc (one_signed_coefficients)
• n-f8c9dbb903f44fdc (hadamard_kernel)
• n-f8c9dbb903f44fdc (real_rooted)