Proof step e-ec629e395a3def0c

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

Theorem

Three-term recurrence criterion [Sze39, §3.3; Fav35] polytool ?

Operation

Theorem check of the node's own rule

{
  "operation": "theorem_check",
  "theorem": "three_term_recurrence"
}

Premises

None: this step is a direct theorem check.

Claims

• { "claim": "real_rooted", "from_index": 0, "region": { "lower": { "closed": false, "value": "-6" }, "upper": { "closed": false, "value": "-2" } } }
• { "claim": "interlacing", "from_index": 1, "kind": "strict", "orientation": "previous_interlaces_next" }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: theorem_check, SHA-256 5840e8f04930313d95df0836e60f47ba034ba0f1ab5d46f077f5a1a85b1b7308, 4,301 bytes (1,259 compressed); download JSON

Cited by

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

References

1. [Fav35] Jean Favard. Sur les polynômes de tchebicheff. C. R. Acad. Sci. Paris, 200:2052–2053, 1935.
2. [Sze39] G. Szegő. Orthogonal Polynomials. Colloquium publications, American Mathematical Society, 1939. doi:10.1090/coll/023