Parabolic convergence regions of branched continued fractions of the special form

  • D.I. Bodnar West Ukrainian National University, Peremohy Square 3, 46009, Ternopil, Ukraine; Ternopil Volodymyr Hnatiuk National Pedagogical University, 2 Maxyma Kryvonosa Str., Ternopil, Ukraine
  • I.B. Bilanyk Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, 3b Naukova str., 79060, Lviv, Ukraine; Ternopil Volodymyr Hnatiuk National Pedagogical University, 2 Maxyma Kryvonosa Str., Ternopil, Ukraine
Keywords: branched continued fraction, convergence, continued fraction, rational approximation
Published online: 2021-11-20

Abstract


Using the criterion of convergence of branched continued fractions of the special form with positive elements, effective sufficient criteria of convergence for these fractions are established. To study the parabolic regions of convergence, the element regions and value regions technique was used. In particular, half-planes are considered as value regions. A multidimensional analogue of Tron's twin convergence regions for branched continued fractions of the special form is established. The obtained results made it possible to establish the conditions for the convergence of the multidimensional $S$-fractions with independent variables.

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How to Cite
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Bodnar D., Bilanyk I. Parabolic Convergence Regions of Branched Continued Fractions of the Special Form. Carpathian Math. Publ. 2021, 13 (3), 619-630.