Like infinite series and infinite products, continued fractions can be considered as arising through the composition of certain types of Moebius transformations. Again like infinite series and products, continued fractions can be used to represent certain types of analytic functions. Contrary to representations by power series, continued fraction representations may converge in regions that contain isolated singularities of the function to be represented, and contrary to representations by infinite products, continued fraction representations in many cases converge very rapidly.