Conversion from special function to continued fraction

Regularized incomplete beta function is defined as

We can use the following formula

  (regular expression)

   in special form

There are several gamma-related functions as well.

Mittag-Leffler function is defined as

in terms of gamma function.

     in special form

Wright function is defined as

We can use the same formula from series to continued faction above. That is

     in special form