Conversion from fraction to continued fraction

Direct and tedious way

(one term)

so

  in special form

(two terms)

so

(three terms)

We can go on but it is too tedious to arrange the terms into  and thereafter. This way is not good for product conversion in general. We need to take some other ways.

We just show the result.

     (regular expression)

　in special form

When j={1,1,1,1, . . .} in particular

     (regular expression)

   in special form