A Lehner continued fraction is a generalized continued fraction of the form
 |
(1)
|
where 
or (2, 
) for 
an irrational number
(Lehner 1994, Dajani and Kraaikamp 2000).
Taking 
at every position gives
 |
(2)
|
where 
is the golden ratio. The constant choice 
gives the limiting expression
 |
(3)
|
This is a rational number at the boundary of the stated irrational number domain. For a positive
integer 
, truncating the negative continued fraction after 
partial numerators gives 
.
