Conversion from series to continued fraction

Recall that

  in special form

as in 0215 at the beginning. When we consider the case with

  in special form

Applying gamma-shaped multipliers repeatedly, we get

Recall that the following consecutive form

in 0114. Then we get

Thus

   (regular expression)

   in special form

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

   (regular expression)

   in special form