A two-variable generalization of the Stieltjes-type continued fraction

AbstractA continued fraction expansion in two variables is described and shown to correspond to a double power series. This continued fraction is a natural generalization of the S-fraction and can be truncated to form a sequence of rational approximants.A simple algorithm is derived for computing the coefficients of the two-variable fraction and the theorem of Van Vleck is adapted to establish the convergence of some simple examples. Numerical results are given comparing the method with Chisholm approximants