Uniformity and Speed of Convergence of Complex Continued Fractions K(an /1)

Using elementary tools and taking advantage of the fascinating underlying geometric behavior, our fundamental goal in this article is to simplify, yet enrich, the catalog of twin convergence region results for continued fractions (c.f.s) of the form (1.1) K ( a n / 1 ) = K n = 1 ∞ a n 1 = a 1 1 + a 2 1 + a 3 1 + ⋯     ,                             0 ≠ a n ∈ ℂ .       https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072126/15070696-a94f-4da5-a117-8ee069a896b3/content/eq3025.tif"/>