Conversion from fraction to continued fraction

Start from the following form

as we got yesterday.

The product of fractions in general is

   (regular expression)

Thus

     (regular expression)

　for  in special form

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

     (regular expression)

   for  in special form

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

     (regular expression)

　  for  in special form