Recall that
or
for any positive value of x
When we set k to each ci, we get
or
before
applying 
The fastest expansion is to use the nearest
k to
. We can use either of
the following:
(1)
Nearest integer or the integer part of the value of 
.
For example, for
we use k=1.
(2)
Nearest fraction 
where
both i and j are integers.
For example, for
we use 
where i=7 and j=5.
The second form has the following variation:
where 