Proof step e-7e402d8f3ce84882

basis_map A007318 → concludes about basis_map_A007318 of Triangle of coefficients of Chebyshev's S(n,x+5) 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

• Triangle of coefficients of Chebyshev's S(n,x+5) polynomials (exponents of x in increasing order). (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 4f2a17e489964f12be74d612b5b57c8cc1ef0387dbf9361b03b16c75fe97293d, 13,345 bytes (2,517 compressed); download JSON

Cited by

• n-1fb3d5de4e4b154d (real_rooted)
• n-1fb3d5de4e4b154d (one_signed_coefficients)
• n-1fb3d5de4e4b154d (hadamard_kernel)
• n-1fb3d5de4e4b154d (interlacing)