Proof step e-c58678c575cc640f

basis_map A007318 → concludes about shift_x_plus_one of Triangle read by rows, A007318 rows repeated four times . JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• Triangle read by rows, A007318 rows repeated four times . (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 9ecc8824800599d48ed0e0231871c3a9cb8ca3565a294b71882a3d22261fd224, 6,945 bytes (1,391 compressed); download JSON

Cited by

• n-714dab5edd34705c (one_signed_coefficients)
• n-714dab5edd34705c (hadamard_kernel)
• n-714dab5edd34705c (real_rooted)