New convergence results for continued fractions generated by four-term recurrence relations

AbstractIn the study of simultaneous rational approximation of functions using rational functions with a common denominator (which can be viewed as the ‘German polynomial’ problem in simultaneous Pade´approximation, cf. [1]) the quest for convergence results lead to the study of generalized continued fractions, a type of Jacobi—Perron algorithm [2,3]. It then becomes important to exploit the connection between the convergence of the generalized continued fraction and the solutions of the associated difference equation (cf. [4,5])