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Most of the known continued fraction expansions of special functions are limit periodic. This means that the classical approximants S n (0) are normally not the best ones to use for approximations. In this paper we suggest a number of approximants S n (w n ) which converge faster. The estimation of the improvement and bounds for the error |f - Sn(wn)| (which we still call the truncation error) are mainly obtained by means of Thron's parabola sequence theorem and the oval sequence theorem.

Even and odd parts of limit periodic continued fractions K( a n /1), a n → a are again limit periodic in most cases. For a = ∞ additional conditions are needed; the particular ones used in the paper imply that the even and odd parts K( c n /1) and K( d n /1) are such that c n → − 1 4 and d n → − 1 4 . Illustrating examples are included.