Some properties of approximations of a branched continued fraction of a special form with non-addition fractional numerators

Antonova Tamara; Vozna Svitlana

Antonova Tamara ¹ , Vozna Svitlana ¹

¹ Department of Applied Mathematics, Lviv polytechnic national university, Lviv, 79007, Ukraine

Keywords: properties of approximations

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Abstract

Properties of approximants for the numerical branched continued fraction of the special form, which is connected with the correspondence problem between a formal double power series and a sequence of the rational approximants of a function of two variables are researched. We establish some sufficient conditions of monotonicity and boundedness for sequences of figured and ordinary approximants of even order for investigated continued fraction with nonpositive partial numerators. Convergence and figured convergence of branched continued fraction of the special form to the same limit are proved under additional restrictions on elements.

References

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ACS Style: Antonova, T.; Vozna, S. Some properties of approximations of a branched continued fraction of a special form with non-addition fractional numerators. Bukovinian Mathematical Journal. 2017, 5
AMA Style: Antonova T, Vozna S. Some properties of approximations of a branched continued fraction of a special form with non-addition fractional numerators. Bukovinian Mathematical Journal. 2017; 5(1-2).
Chicago/Turabian Style: Tamara Antonova, Svitlana Vozna. 2017. "Some properties of approximations of a branched continued fraction of a special form with non-addition fractional numerators". Bukovinian Mathematical Journal. 5 no. 1-2.

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