Truncation Error Bounds for Continued Fractions K(an/1) with Parabolic Element Regions

Value regions for continued fractions are intimately related to such questions as convergence, truncation error analysis and numerical stability. The present paper introduces a new family of value regions corresponding to parabolic element regions for continued fractions K(an/1). The value regions are used to obtain lens-shaped inclusion regions and truncation error bounds. The results generalize and bring into focus connections between some earlier work by Thron and others on parabolic convergence regions and by Henrici and Pfluger on Stieltjes fractions.