Consider the equation
.
Providing for all solutions of
yields three iterators:

where

Furthermore, all solutions can be generated by simply using different
values of *n*.
For the first equation, values
will yield the even
numbered roots, whereas values
will yield the
remaining roots when used in the second equation.
Other values of *n* diverge.
(The asymmetry comes from the positive sign on the first
;
the iterator
would supply the same set of roots with
).
The solution obtained is unrelated to the initial guess used;
almost any starting value acceptable to the
converges to the
same root for a given choice of iterator and *n*.