Truncation-error bounds for the 1-periodic branched continued fraction of special form

Abstract

Truncation-error bounds for the 1-periodic continued fraction of special form are established at the following conditions: if first element of the fraction belongs to complex plain with the cut ($−\infty;−1/4$] and the sum of modules of other elements is limited by a certain number; if elements belong to their respective parabolic regions or union of that parabolic regions and all their modules, except of the first one, are limited.