Proof step e-6f81123042c063ba

theorem_check three_term_recurrence → concludes about Triangle of coefficients of n!*(1 - x)^n*L_n(x/(1 - x)), where L_n(x) is the Laguerre polynomial. 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": 1, "region": {} }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: theorem_check, SHA-256 731284dcbe8c88e474f8bc300f4d47fb6d8085f9b6a9be80f0234a8109ca1b0a, 2,791 bytes (1,091 compressed); download JSON

Cited by

• n-db839974123087ee (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