SOME CIRCULAR REGIONS OF CONVERGENCE FOR BRANCHED CONTINUED FRACTIONS OF A SPECIAL FORM

摘要

For branched continued fractions of a special form, we obtain circular regions of convergence. These regions are related to the multidimensional generalizations of some well-known theorems (W. Leighton, H. S. Wall, W. J. Thron, L. J. Lange, J. Mc Laughlin, and N. J. Wyshinski) on twin convergence regions for continued fractions. In the case where a branched continued fraction is transformed into a continued fraction (N = 1), the obtained circular regions can of convergence be wider (under certain conditions imposed on the parameters) than some known twin convergence regions for continued fractions.