Proof step e-5437345511af69a3

theorem_check three_term_recurrence → concludes about chebyshev_t 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": "-1" }, "upper": { "closed": false, "value": "1" } } }
• { "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 7ee55dd53825b530984a01921df5e270bdc69f6b05187dfaa0645d9dff07315e, 4,272 bytes (1,249 compressed); download JSON

Cited by

• n-9ae8d431f7b33f22 (interlacing)
• n-9ae8d431f7b33f22 (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