Proof step e-23c3ede392db8800

basis_map A007318 → concludes about basis_map_A007318 of Riordan array (1, 2+2x). 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, 2+2x). (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 706b70e07430b64d469bff686c55d7ee5679709af181e762c55b645945e790bf, 11,661 bytes (2,186 compressed); download JSON

Cited by

• n-002f74523f94b1c9 (real_rooted)
• n-002f74523f94b1c9 (one_signed_coefficients)
• n-002f74523f94b1c9 (hadamard_kernel)