Proof step e-ba56344dd1f68fd7

basis_map A013609 → concludes about basis_map_A013609 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": "A013609",
  "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 c4e4c3c7a68f2ead4a91bab8aa47044c00e73e8dc2c16b208378f52cb30faf13, 11,582 bytes (2,152 compressed); download JSON

Cited by

• n-30551c14ec291558 (real_rooted)
• n-30551c14ec291558 (one_signed_coefficients)
• n-30551c14ec291558 (hadamard_kernel)