Rogers-Ramanujan continued fraction

 

We defined

 

 

as in 0412. In addition, we here define

 

   for |ab|<1

 

Then the following relation holds.

 

 

Using these functions, we can express P and Q in Ramanujan’s identities.

 

and

 

where P=Q. Here,

  in special form of continued fraction.

 

If we use

 

  in special form,

 

we will have

 

 and