Proof step e-19ca7a5e6e7a3cfc

theorem_check three_term_recurrence → concludes about Triangle read by rows: T(k,s) = ((2*k+1)/(2*s+1))*binomial(k+s,2*s), 0 <= s <= k. 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": { "lower": { "closed": false, "value": "-4" }, "upper": { "closed": false, "value": "0" } } }
• { "claim": "interlacing", "from_index": 2, "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 c03fe8c5492a79fb2ab1bf06b0e98fadbee2a114d5476c6b06c9b321f73a1fcc, 4,289 bytes (1,272 compressed); download JSON

Cited by

• n-318700a428d7b97b (interlacing)
• n-318700a428d7b97b (one_signed_coefficients)
• n-318700a428d7b97b (hadamard_kernel)
• n-318700a428d7b97b (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