Continued fraction for

Recall that

 
mentioned yesterday, we can use other points to be evaluated. For example,
 

 
we can say that
 

 
We can get more expansions from many other points.
 
Basically, we can do the same thing from any inverse of trigonometric functions. 
 
We can use any expansion without Pi inside. We can use the following expansions:
 
 for 
 
and
 
 for 
 
and
 
 for 
 
mentioned in 0303 and 0305.
 

To convert these, we usually use the following formula

(regular expression)

 in special form
 
We can use the following relations:
 



 
Since
 
 in special form
or

 
after applying rule of sings (down->front&next) to every two terms and then 
 
applying it again(both->next, down->front&next). This is exactly the same as 
 
what we got from pi/4=arctan(1).