 Convergence problem

In the analytic theory of continued fractions, the convergence problem is the determination of conditions on the partial numerators "a""i" and partial denominators "b""i" that are sufficient to guarantee the convergence of the continued fraction

This convergence problem for continued fractions is inherently more difficult than the corresponding convergence problem for infinite series.When the elements of an infinite continued fraction consist entirely of positive real numbers, the determinant formula can easily be applied to demonstrate when the continued fraction converges.