Most irrational numbers do not have any periodic or regular behavior in their continued fraction expansion.

Divide by and write out the result as a partial fraction expansion.

It is also unknown if there are algebraic numbers with unbounded coefficients in their continued fraction expansion.

Euler proved this by showing that its simple continued fraction expansion is infinite.

The simple continued fraction expansion of Champernowne's constant has been studied as well.

That is, the minimal forms, which includes the ladder networks obtained by Stieltjes's continued fraction expansion.

In modern terms, the theorem is that a real number with an infinite continued fraction expansion is irrational.

If the denominator of G(s) contains repeated factors, the partial fraction expansion is slightly modified.

These approximations can be derived from the continued fraction expansion of :

A continued fraction expansion of the complementary error function is: