asympBound_def' — Mathlib

English

The asymptotic bound is given by asympBound(n) = n^p(a,b) + sumTransform(p(a,b)) g 0 n, which describes the Akra–Bazzi growth.

Русский

Асимптотическое ограничение задаётся выражением asympBound(n) = n^{p(a,b)} + sumTransform(p(a,b)) g 0 n, описывая рост Ака-Бази.

LaTeX

$$$\text{asympBound}(g,a,b;n) = n^{p(a,b)} + \text{sumTransform}(p(a,b),g;0,n)$$$

Lean4

theorem asympBound_def' {α} [Fintype α] (a b : α → ℝ) {n : ℕ} :
    asympBound g a b n = n ^ p a b * (1 + (∑ u ∈ range n, g u / u ^ (p a b + 1))) := by
  simp [asympBound_def, sumTransform, mul_add, mul_one]

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