Proof step e-7a44d9ed78450a4e

basis_map A007318 → concludes about shift_x_plus_one of Riordan array (1-x,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-x,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 6da10e6e38a6daca6683d710d4aee9078a7ae20280a4cda704026e0562758cd5, 6,895 bytes (1,394 compressed); download JSON

Cited by

• n-21d2f90cb223c8f5 (one_signed_coefficients)
• n-21d2f90cb223c8f5 (hadamard_kernel)
• n-21d2f90cb223c8f5 (real_rooted)