Abstract
Using the majorant fraction method and equivalent transformations, we obtain analogues of the Śleszyński–Pringsheim convergence for two-dimensional continued fractions.
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References
D. I. Bondar, Branching Continued Fractions [in Russian], Naukova Dumka, Kyiv (1986).
D. I. Bondar, “Convergence criteria of the Pringsheim type for branching continued fractions, ” Ukrain. Mat. Zh., 41, No. 11, 1559–1563 (1989); English transl. in Ukrain. Math. J.
H. Y. Kuchminska, “Corresponding and adjoined branching continued fractions for a double power series, ” Dop. Akad. Nauk Ukr. SSR, Ser. A, 7, 614–618 (1978).
H. I. Kuchminska, “Convergence criteria for two-dimensional continued fractions with complex components, ” in: Methods of investigation of differential and integral operators [in Russian], Naukova Dumka, Kyiv, pp. 122–127.
I. V. Śleszyński, “On the convergence of continued fractions, ” Notes of the Novosibirsk Mathematical Society of Natural Science, 10, 201–255 (1989).
H. S. Wall, Analytic Theory of Continued Fractions, Van Nostrand, New York (1948).
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Kuchminska, H.U. Analogs of the Śleszyński–Pringsheim Criteria for Two-Dimensional Continued Fractions. Journal of Mathematical Sciences 107, 3562–3566 (2001). https://doi.org/10.1023/A:1011934005295
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DOI: https://doi.org/10.1023/A:1011934005295