2019
Том 71
№ 8

All Issues

Dmytryshyn R. I.

Articles: 2
Article (Ukrainian)

Multidimensional associated fractions with independent variables and multiple power series

Bodnar D. I., Dmytryshyn R. I.

↓ Abstract

Ukr. Mat. Zh. - 2019. - 71, № 3. - pp. 325-349

We establish the conditions of existence and uniqueness of a multidimensional associated fraction with independent variables corresponding to a given formal multiple power series and deduce explicit relations for the coefficients of this fraction. The relationship between the multidimensional associated fraction and the multidimensional $J$ -fraction with independent variables is demonstrated. The convergence of the multidimensional associated fraction with independent variables is investigated in some domains of the space $C^N$. The expansions of some functions into the corresponding two-dimensional associated fraction with independent variables are constructed and the efficiency of approaching of the obtained expansions by approximants is shown.

Article (Ukrainian)

Associated Branched Continued Fractions with Two Independent Variables

Dmytryshyn R. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2014. - 66, № 9. - pp. 1175–1184

An algorithm for the expansion of a given formal double power series in the associated branched continued fraction with two independent variables is constructed and the conditions for the existence of this expansion are established.