Theorems · Theorem · real analysis

Complex.isTheta_cpow_rpow

∀ {α : Type u_1} {l : Filter α} {f g : α → ℂ},
  (Filter.IsBoundedUnder (fun x1 x2 => x1 ≤ x2) l fun x => |(g x).im|) →
    (∀ᶠ (x : α) in l, f x = 0 → (g x).re = 0 → g x = 0) → (fun x => f x ^ g x) =Θ[l] fun x => ‖f x‖ ^ (g x).re

Defined in

Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics

Cited by

1 results in Mathlib

Foundations

Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound