asympBound — Mathlib

English

The sumTransform is defined by the rule: sumTransform(p,g,n0,n) = n^p ∑_{u ∈ Ico(n0,n)} g(u)/u^{p+1}.

Русский

SumTransform задаётся правилом: sumTransform(p,g,n0,n) = n^p ∑_{u ∈ Ico(n0,n)} g(u)/u^{p+1}.

LaTeX

$$$\text{sumTransform}(p,g;n_0,n) = n^p \cdot \sum_{u \in \mathrm{Ico}(n_0,n)} \dfrac{g(u)}{u^{p+1}}$$$

Lean4

/-- The asymptotic bound satisfied by an Akra-Bazzi recurrence, namely
`n^p (1 + ∑_{u < n} g(u) / u^(p+1))`. -/
noncomputable def asympBound (n : ℕ) : ℝ :=
  n ^ p a b + sumTransform (p a b) g 0 n

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