Proof step e-23f81812d1886d3d

basis_map A013609 → concludes about basis_map_A013609 of Twice Pascal's triangle A007318: T(n,k) = 2*C(n,k). JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013609",
  "operation": "basis_map"
}

Premises

• Twice Pascal's triangle A007318: T(n,k) = 2*C(n,k). (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 a0c95427e0e679335e940808d364b25cbeeb7b19431f74a725626f26289dcf86, 6,855 bytes (1,391 compressed); download JSON

Cited by

• n-652b5ddc7f7231b8 (real_rooted)
• n-652b5ddc7f7231b8 (one_signed_coefficients)
• n-652b5ddc7f7231b8 (hadamard_kernel)