Proof step e-e0e39e6ac529ed26

obreschkoff_combination → concludes about obreschkoff_combination of Triangle related to the o.g.f.s. of the right-hand columns of A130534 (E(x,m=1,n)). JSON

Theorem

Hermite–Kakeya–Obreschkoff theorem [Obr63; Fis06, Thm 1.43] ?

Operation

Obreschkoff combination Pₙ + Pₙ₊₁

{
  "operation": "obreschkoff_combination"
}

Premises

• Triangle related to the o.g.f.s. of the right-hand columns of A130534 (E(x,m=1,n)). (sequence)
  uses: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, +inf)
• Triangle related to the o.g.f.s. of the right-hand columns of A130534 (E(x,m=1,n)). (sequence)
  uses: Rows P_(m-1), P_m interlace (weak, unordered) for every m >= 1

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: obreschkoff_combination, SHA-256 cdd52d867dc919f0f858ae0cab8c29f3d5a4ba0e2f325fe48e15a0f9addde57a, 13,117 bytes (2,829 compressed); download JSON

Cited by

• n-770bc0f5eb42b52a (real_rooted)

References

1. [Fis06] Steve Fisk. Polynomials, roots, and interlacing. arXiv:math/0612833. arXiv
2. [Obr63] Nikola Obreschkoff. Verteilung und berechnung der nullstellen reeller polynome. Hochschulbücher für mathematik, VEB Deutscher Verlag der Wissenschaften, 1963.