Proof step

Three-term recurrence criterion

Theorem check of the sequence's own rule three term recurrence

Concludes: hadamard_factor parent of Triangle read by rows: t(n,m) = binomial(2*n,2*m) * binomial(n,m).
Premises: none: a direct theorem check
Theorem: [Sze39, §3.3; Fav35] polytool ?
Checked: polytool replayed · Lean not attempted

Technical details

Step id

e-399c824d392e2d5f · JSON

Operation

Theorem check of the sequence's own rule

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

Claims

{
  "claim": "real_rooted",
  "from_index": 1,
  "region": {
    "upper": {
      "closed": false,
      "value": "0"
    }
  }
}

{
  "claim": "interlacing",
  "from_index": 2,
  "kind": "strict",
  "orientation": "previous_interlaces_next"
}

Certificate

theorem_check, SHA-256 673c2f593f8c93df0b51a49cba45728d2a48e7578721d08f86abf9bc883dc67e, 4,361 bytes (1,317 compressed); download

polytool replayed the certificate when the step was written.

Cited by

References

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