Conversion from series to continued fraction

 

We use one of yesterdayfs results. That is,

 

  in special form

 

We can say that

 

  (regular expression)

  in special form

 

Recall that

 

@

We then have

 

 

Applying gamma-shaped location of multipliers repeatedly,

 

 .

 .

 .

 

Thus

 

  (regular expression)

   in special form

 

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

 

   (regular expression)

   in special form