Continued fractions. Vol. 1: Convergence theory. 2nd ed

Periodiccontinuedfractionsarewellunderstood.Wecandeterminewhentheyconverge,whentheydiverge,theirvaluesiftheyconvergeandtheasymptoticbehavioroftheirtailsequences.Indeed,itisallamatterofiterationsoflinearfractionaltransformations,andwehaveclosedexpressionsfortheirapproximantsSn(w).