Numer. Math. 46, 541-569 (1985) Numerische MathemalJk 9 Springer-Verlag 1985 Truncation Error Bounds for Limit-Periodic Continued Fractions K(a.]l) With lim a. = 0* Christopher Baltus and William B. Jones Department of Mathematics, University of Colorado, Boulder, Colorado 80309, USA Summary. Truncation error bounds are developed for continued fractions K(aJ1) where la, I < 1/4 for all n sufficiently large. The bounds are particu- larly suited (some are shown to be best) for the limit-periodic case when lim a, = 0. Among the principal results is the following: If l a.I < ~/np for all n sufficiently large (with constants ~>0, p>0), then {f-fml<C[D/(m +2)3 ptm§ for all m sufficiently large (for some constants C>0, D>0). Here f denotes the limit (assumed finite) of K(a,/1) and fm denotes its ruth approximant. Applications are given for continued fraction expansions of ratios of Kummer functions 1F1 and of ratios of hypergeometric functions 0F1. It is shown that p=l for ~F~ and p=2 for oF~, where p is the parameter determining the rate of convergence. Numerical examples in- dicate that the error bounds are indeed sharp. Subject Classifications: AMS(MOS): 65D15; CR: G12. I. Introduction This paper deals with bounds for the truncation error If--fmJ obtained when a continued fraction =-i-+ 1 + 1 +"" converging to a finite limit f is replaced by its ruth approximant fro" Attention is focused on the limit periodic case in which lira a, = 0. (1.2) Unless stated otherwise, it is assumed throughout that in (1.1), a,=l=0 for all n>=l. * Research supported in part by the National Science Foundation under Grant MCS-8202230 and DMS-8401717