Continued fractions and series (Q1900888)

Generally it is difficult to compute the simple continued fraction expansion for a real irrational number which is defined by some other expression. But there are some known results on infinite series of rational numbers of rather peculiar type whose sequence of partial denominators in their continued fraction shows a definite pattern, being periodic or palindromic in some portions. See \textit{A. J. van der Poorten} and \textit{J. Shallit} [J. Number Theory 40, 237-250 (1992; Zbl 0753.11005)]\ for one of the recent papers in this field. In the paper under review the authors tie together previous results and provide many more interesting examples. They also show that Newton's method, with suitable initial values, produces convergents for the simple continued fraction expansion of quadratic irrationals.