Proof step e-0c1e3d0b7f1bd773

theorem_check three_term_recurrence → concludes about Triangle read by rows: T(n,k) = binomial(2n+1, 2k+1). 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": {} }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: theorem_check, SHA-256 05cde71e32ebeaafad3ebe80852a052db7da3c2a443190cca30cf8eb427382b9, 2,697 bytes (1,052 compressed); download JSON

Cited by

• n-c30cb06ad75c5e21 (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