Further results on convergence acceleration for continued fractions 𝐾(𝑎_{𝑛}/1)

Abstract

Abstract. If K(a'"/\) is a convergent continued fraction with known tails, it can be used to construct modified approximants/"* for other continued fractions K(a"/\) with unknown values. These modified approximants may converge faster to the value/of K(an/\) than the ordinary approximants/, do. In particular, if a" -a'" -» 0 fast enough, we obtain \f -f*\/\f -f"\-* 0; i.e. convergence acceleration, the present paper also gives bounds for this ratio of the two truncation errors, in many cases.