Modified Rogers-Ramanujanfs and other continued fractions

 

There are some misunderstandings to expand continued fractions.

 

 

only for around q=1 and|a|<|b|. This does not hold all over the domain of |q|<1.

 

However, the following relation

 

 

only for |q|<1 and|a|<|b|.

 

Here, we just apply the gamma-shaped multipliers of q, q2,q3,. . . in order.

 

Thus, we cannot say that

 

 

only for |q|<1 and|a|<|b|. That is one big problem.

 

 

Bauer Muir transformation

 

 

for

   /=0  and k=1,2,3,c

 

is not an identity but an approximate that is going to be the same on average.

 

Some of modified Rogers-Ramanujanfs and other continued fractions are identities.

 

Some of them are just approximations around a certain point or even based on some

 

wrong specification. They forge to explain or verify some wrong approximations.