Proof step e-9c2f7b8109ebb5e1

basis_map A007318 → concludes about Triangle of coefficients of Chebyshev's S(n,x+4) polynomials (exponents of x in increasing order). JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• A convolution triangle of numbers based on A001906 (even-indexed Fibonacci numbers). (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" } } }
• { "claim": "interlacing", "from_index": 1, "kind": "weak", "orientation": "unordered" }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 5c0641eeb3a9cd41b1ba05ed992465ace15bdce89402f0562dc712ea262595a0, 13,345 bytes (2,516 compressed); download JSON

Cited by

• n-30cb3cad216ed189 (one_signed_coefficients)
• n-30cb3cad216ed189 (hadamard_kernel)
• n-30cb3cad216ed189 (real_rooted)
• n-30cb3cad216ed189 (interlacing)