Computer use in continued fraction expansions

Abstract

In this study, the use of computers is demonstrated for the rapid expansion of a general regular continued fraction with rational elements for √ C + L \surd C + L , where C C and L L are rational numbers, C C positive. Formulas for the expansion are derived. Conditions for the periodicity are considered. A Fortran program for the algorithms is given, as well as sample continued fraction expansions. Up to the present, practically all studies have been concerned with continued fractions with partial numerators ± 1 \pm 1 and partial denominators positive integers, due to difficulties in calculation. But now the use of computers makes possible the study of a much greater variety of continued fraction expansions.