On a Khovanskii transformation for continued fractions

摘要

Some aspects of a transformation for continued fractions due to Khovanskii are studied. It is shown that the transformation does not in general establish an identity, but has many interesting properties. It permits to transform some difficult continued fractions into suitable ones. Its even part is identical to the even part of Sn(−12) modification. It may also give acceleration for some slow continued fractions.