Shrinking the period length of quasi-periodic continued fractions

Extending the work of Burger et al., here we show that every quasi-periodic simple continued fraction alpha can be transformed into a quasi-periodic non-simple continued fraction having period length one. Moreover, a certain kind of quasi-periodic non-simple continued fraction is equivalent to a quasi-periodic N-continued fraction. The results of this paper follow from arguments of Burger et al. but we apply our version to offer new continued fractions for certain classes of real numbers. (C) 2008 Elsevier Inc. All rights reserved.