erdos_516.limsup_ratio_eq_one_of_hasFabryGaps_ofFiniteOrder

Let `f = ∑ aₖzⁿₖ` be an entire function of finite order such that `nₖ / k → ∞`. Then `limsup (fun r => ratio r f) atTop = 1`. This is proved in [Fu63].

theorem erdos_516.limsup_ratio_eq_one_of_hasFabryGaps_ofFiniteOrder {f : ℂ → ℂ} {n : ℕ → ℕ}
    (hn : HasFabryGaps n) {a : ℕ → ℂ} (ha : ∀ n, a n ≠ 0)
    (hfn : ∀ z, HasSum (fun k => a k * z ^ n k) (f z)) (hf : OfFiniteOrder f) :
    limsup (fun r => ratio r f) atTop = 1

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