Proof step e-4baab92f0107de2d

preserver_image mobius, shift 0 → concludes about mobius_x_over_x_plus_one of Triangle of coefficients of Chebyshev's S(n,x+4) polynomials (exponents of x in increasing order). JSON

Theorem

Affine, reversal and Möbius substitutions (elementary) polytool ?

Lean (RealRooted): route fTransform RealRooted.splits_fPolynomial

Operation

Image under a real-rootedness preserver

{
  "index_shift": 0,
  "operation": "preserver_image",
  "operator": "{\"shape\":\"mobius\",\"a\":\"1\",\"b\":\"0\",\"c\":\"1\",\"e\":\"1\",\"schedule\":{\"first_index\":0,\"first_degree\":0,\"step\":1}}"
}

Premises

• Triangle of coefficients of Chebyshev's S(n,x+4) polynomials (exponents of x in increasing order). (sequence)
  uses: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-6, -2)

Claims

• { "claim": "real_rooted", "from_index": 0, "region": { "lower": { "closed": true, "value": "-1" }, "upper": { "closed": false, "value": "-2/3" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: preserver_image, SHA-256 d139380394413725f4e3ccdded1a1e84320d8631c3ad9cd8b6de016730095c14, 17,419 bytes (3,420 compressed); download JSON

Cited by

• n-5038739ef66fadea (real_rooted)
• n-5038739ef66fadea (one_signed_coefficients)
• n-5038739ef66fadea (hadamard_kernel)