On the convergence of algebraic continued fractions whose coefficients have limiting values

in which U^z), Vt(z) denote certain polynomials with which we need not concern ourselves here. The object of the following note is to investigate the convergence of these three classes of continued fractions upon the hypothesis that the coefficients an,bn, ■ --,gn have limiting values for n = oo. The results obtained below for the first two types of continued fractions are in no wise dependent upon the value of p2 nor upon the nature of the polynomials Ui, Vi, neither are they affected by the introduction of a finite number of irregularities into the continued fraction—that is to say, by the presence of a finite number of partial numerators or denominators of degree higher than the normal. This is not true of the third type of continued fractions.