Branch-safe annular domain for the weighted-root integrand
DefinitionweightedRootBranchSafeRegionbranch-cutcomplex-analysisdomainkeyhole-contour
The branch-safe domain consists of the annulus r < |z| < R in which every shifted factor z-a_i lies in the principal-power slit plane.
Definition code
import Mathlib
open scoped BigOperators
def weightedRootBranchSafeRegion (n : ℕ) (a : ℕ → ℝ) (r R : ℝ) : Set ℂ :=
{z | r < ‖z‖ ∧ ‖z‖ < R ∧ ∀ i < n, z - (a i : ℂ) ∈ Complex.slitPlane}
Source
Common domain of the principal complex powers (z-a_i)^{w_i} and the reciprocal factor 1/z.