Conversion from special function to continued fraction

Infinite product of reciprocal of gamma function is

We can use the following formula

     (regular expression)

   in special form

as in 0220.

Beta function is defined as

This function is closely related to gamma function. That is

Its infinite product is

We can use the following formula

     (regular expression)

There are several series to expand this beta function.

One way is

       for integers of x and y

where  and .

Another way is

                 for integers of x and y

We can use the following formula

  (regular expression)

   in special form