Proof step

Liu–Wang theorem for three-term recurrences

Theorem check of the sequence's own rule liu wang three term

Concludes: Triangle read by rows giving coefficients of the trigonometric expansion of sin(n*x).
Premises: none: a direct theorem check
Theorem: [LW07, Thm 2.1, Thm 2.3, Cor 2.4, Prop 3.3] polytool ?
Lean: RealRooted RealRooted.MaWang.strictInterl_of_interlaces_evalCoeff_nonpos
Checked: polytool replayed · Lean not attempted

Technical details

Step id

e-7012213a5f97c642 · JSON

Operation

Theorem check of the sequence's own rule

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

Claims

{
  "claim": "real_rooted",
  "from_index": 1,
  "region": {}
}

Certificate

theorem_check, SHA-256 a45922750cc24ed50d0999312e9320692499ff1091a2fcd297d488e87c6ab439, 3,549 bytes (1,379 compressed); download

polytool replayed the certificate when the step was written.

Cited by

References

[LW07] Lily L. Liu and Yi Wang. A unified approach to polynomial sequences with only real zeros. Advances in Applied Mathematics, 38(4):542–560, May 2007. doi:10.1016/j.aam.2006.02.003