Conversion from series to continued fraction

Recall that

   (regular expression)

   in special form

mentioned yesterday. We consider

We can regard it as

   in special form

Thus

  (regular expression)

      in special form

Recall that

  (regular expression)

   in special form

in 0216. We here consider

This can be regarded as

   (regular expression)

Directly applying the formula above, we get

Applying gamma-shaped multipliers repeatedly, we get

 .

 .

 .

Thus

     (regular expression)

     in special form